Which statement is true for log3(x+1)= 2?

On solving the provided question, we can say that By BODMAS, 2.4of4.5-5.6/1.4+3.8*2 => 10.8-5.6/1.4+3.8*2 => 10.8-4+3.8*2 = > 14.4

The abbreviation BODMAS aids kids in recalling the hierarchy of mathematical operations (the correct order for solving math problems). The acronym BODMAS is made up of the following terms: B Bracket, O Degree (Power/Exponent or Root), D Division, M Multiplication, A Addition, and S Subtraction. BODMAS is also referred to as PEDMAS in some locales. This symbolizes exponents, division, multiplication, addition, and subtraction. It also represents parentheses. The BODMAS rule states that parentheses must be handled first, followed by powers or roots (i.e., of), divisions, multiplications, additions, and lastly subtractions. While he is known as BODMAS in India and the UK, PEMDAS is primarily utilized in the US. However, they are identical to one another. The parentheses, order, and order of the operations of addition, subtraction, multiplication, and division are the same for the two rules.

By BODMAS

2.4of4.5-5.6/1.4+3.8*2

10.8-5.6/1.4+3.8*2

10.8-4+3.8*2

10.8-4+7.6

14.4

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The numeric value of the expression -b + 8x when b = 5 and x = -6 is given as follows:

-53.

To find the numeric value of a function or of an expression, we replace each instance of the variable/variables in the function or in the expression by the value/values at which we want to find the numeric value.

In this problem, the expression is given as follows:

-b + 8x.

The values at which the numeric value is to be found are:

b = 5, x = -6.

Hence:

Thus the numeric value of the expression is obtained as follows:

-5 + 8(-6) = -5 - 48 = -53.

The problem is given by the image at the end of the answer.

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The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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Answer:

  (b)  22 in

Step-by-step explanation:

You want the perimeter of a rectangle with side lengths 4 inches and 7 inches.

The perimeter of a rectangle is the sum of the lengths of its sides. Your rectangle has two sides that are 4 inches, and two sides that are 7 inches. The perimeter is the sum of these lengths:

  P = 4 in + 4 in + 7 in + 7 in

  P = 22 in

The perimeter of the rectangle is 22 inches.

__

Additional comment

We can save a math operation by recognizing the sum can be arranged to ...

  P = (4 in +7 in) +(4 in +7 in) = 2(4 in +7 in)

This is evaluated using one sum and one product, rather than the three sums we need if we simply add the lengths of the four sides.

This is why the usual formula for the perimeter of a rectangle is ...

  P = 2(L +W)

Answer:

General form \(x^{2}\) + \(y^{2}\) -2x -2t -14 = 0

Step-by-step explanation:

\(\sqrt{(x-1)^{2} +(y-1)^{2} }\) = 4  Square both sides

\((x-1)^{2}\) + \((y-1)^{2}\) = \(4^{2}\)

\(x^{2}\) - 2x + 1 + \(y^{2}\) -2y + 1 = 16  Combine like terms

\(x^{2}\) + \(y^{2}\) -2x - 2y +2 = 16  Subtract 16 from both sides

\(x^{2}\) + \(y^{2}\) -2x -2y -14 = 0

Let's use the conditional probability formula to calculate the probability that Luis makes both free throws:

P(both free throws) = P(makes first) * P(makes second | makes first)

We are given that:

P(makes first) = 0.75

P(makes second | makes first) = 0.85

So we can substitute these values in the formula:

P(both free throws) = 0.75 * 0.85

P(both free throws) = 0.6375

Therefore, the probability that Luis makes both free throws is 0.6375, or 0.638 rounded to the nearest thousandth.

Answer:

4 percent

Step-by-step explanation:

because the new value is greater than the old value

The Answer is  4 percent

The given statement is:

41 fewer than the quantity t times 307 is equal to n.

The equation is given by:

This question is about piecewise-defined function whereby the statements given are defined by two or more equations.

We need to translate the statement given in the question into inequality equations.

Piecewise-defined function for C(x) are;

C(x) = $25 {if 0 ≤ x ≥ 250}

C(x) = $25 + $0.20x {if x > 250}

We are told that the phone company offers a monthly plan that costs $25 and that this plan includes a maximum of 250 minutes.

Since the piece wise function for the cost is C(x), where x is the number of minutes in a month, then;

C(x) = $25 {if 0 ≤ x ≥ 250}

Also, we are told that there are charges of $0.20 per minute above 250 minutes.

Thus, we can write;

C(x) = $25 + $0.20x {if x > 250}

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A good practice to remember when adding transitions to a presentation is to ensure that they are purposeful, consistent, and enhance the overall flow of the presentation.

Purposeful: Use transitions to guide the audience through your key points and ideas, making sure they complement the content and contribute to the overall message.
Consistent: Maintain a consistent style of transitions throughout your presentation to maintain a cohesive look and feel. Avoid using too many different types of transitions, as this may be distracting.
Enhance flow: Transitions should help create a smooth flow between slides and ideas, making it easy for the audience to follow your presentation. Avoid using abrupt or overly flashy transitions that may interrupt the natural progression of your content.

finally, Test your presentation with the transitions to make sure they enhance the overall flow and comprehension of your message.

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The class had cleaned x × A square miles before lunch.

Let's assume that the area of the park is A square miles, and the portion of the park cleaned by Mai's class before the lunch break is represented by x (a fraction or decimal between 0 and 1).

If the class had cleaned x portion of the park, then the area they had cleaned is x times the total area of the park:

Area cleaned before lunch = x × A

Since x represents a fraction or decimal, multiplying it by the total area A gives us the corresponding portion of the park that was cleaned.

Let's say the park has an area of A square miles, and the area that Mai's class cleaned up before lunch is denoted by the number x (a fraction or decimal between 0 and 1).

If the class had cleaned a certain percentage of the park, their cleaned area would be x times the park's overall area:

Before lunch, the area was cleaned = x A

We may calculate the proportion of the park that was cleaned by multiplying x by the entire area A because it indicates a fraction or decimal.

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Answer:

14:46= 0.3

Step-by-step explanation:

Ratios can be expressed as a decimal, fraction or a math expression as above. (2 weeks is 14 days.)

The values of x and y are given as follows:

The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.

The bases for this problem are given as follows:

2 and x.

The altitude is given as follows:

6.

Hence the length x is given as follows:

2x = 6²

2x = 36

x = 18.

Applying the Pythagorean Theorem, the length y is given as follows:

y² = 18² + 6²

y² = 360

\(y = \sqrt{36 \times 10}\)

\(y = 6\sqrt{10}\)

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Answer:

Step-by-step explanation:

Use the formula A=Pe^rt to solve. A is the final amount, P is the initial amount, r is rate of interest, and t is time.

Therefore,

A=10000e^(0.07)(18)

A=35254.21

Answer:

the answer is A

Step-by-step explanation:

have a good day

Answer:

8.

Step-by-step explanation:

Constant = Constant

Answer:

Step-by-step explanation:

The line segment joining two points P and Q can be represented by the equation of a straight line in the form y = mx + b, where m is the slope and b is the y-intercept.

To find the equation of the line, we need to find the slope, which can be calculated using the formula:

m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the points P and Q, respectively.

In this case, the coordinates are:

P = (-3, 2) and Q = (5, 7)

So, the slope is:

m = (7 - 2) / (5 - (-3)) = 5 / 8

Next, we can use either of the points to find the y-intercept. Let's use point P:

b = y - mx, where y and x are the y and x coordinate of the point, respectively.

In this case,

b = 2 - m * (-3) = 2 - (5/8) * (-3) = 2 + 15/8 = 89/8

So, the equation of the line joining the points P and Q is:

y = (5/8)x + 89/8

Now, to find the point where the line crosses the y-axis, we need to find the x-coordinate of the point where y = 0.

So, we have:

0 = (5/8)x + 89/8

Solving for x, we get:

x = -(89/8) / (5/8) = -89 / 5

This means that the line crosses the y-axis at the point (-89/5, 0). To find the ratio in which the line segment is divided by the y-axis, we need to find the ratio of the distance from the y-axis to point P to the distance from the y-axis to point Q.

Let's call the point of intersection with the y-axis R. The distances are then:

PR = (3, 2) and QR = (5 - (-89/5), 7)

The ratio of the distances is then:

PR / QR = (3, 2) / (5 - (-89/5), 7) = 3 / (5 + 89/5) = 3 / (94/5) = 15/47

So, the line segment joining the points P and Q is divided by the y-axis in the ratio 15:47.

The first hour there will be 18 costumers that will order Turkey sandwiches

Probability

First, we want to find the probability of having a costumer who choose Turkey sandwich.

In order to find it, we calculate the ratio of turkey sandwiches over the total number of orders.

Turkey sandwiches: 180

Total number of orders: 160 + 100 + 180 + 60 = 500

Ratio = turkey / total

Ratio = 180 / 500 = 0.36

Then, the probability of having a costumer who choose Turkey sanwich is

P(T) = 0.36 = 36%

Secondly, in order to find the 36% of 50, we just multiply 0.36 by 50:

Hence , the first hour there will be 18 costumers that will order Turkey sandwiches

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Answer:

4

Step-by-step explanation:

Im  smart and goatified

Answer:4x^2–3>0

Step-by-step explanation:

Answer:

The average occupancy rate for the past three nights is of 86.49%.

Step-by-step explanation:

We want to find the average occupancy rate, as a percentage.

You've sold 101 rooms, 98 rooms, and 102 rooms over the past 3 days.

So the mean number of rooms sold during the past 3 days is given by:

\(A = \frac{101 + 98 + 102}{3} = \frac{301}{3} = 100.33\)

Average rate:

\(R = \frac{100.33*100}{116} = 86.49\)

The average occupancy rate for the past three nights is of 86.49%.

The correct answer is that the data set {3, 7, 4} is represented in the given histogram.(option-a)

The given histogram represents the number of children in each age group who need to travel to school. Since the histogram has only three bars, we can conclude that there are only three age groups.

The first bar represents children aged 5-10, of which there are 3. The second bar represents children aged 11-13, of which there are 7. The third bar represents children aged 14-18, of which there are 4.

Therefore, the data set that is represented in the histogram is:

{3, 7, 4}

None of the other data sets given match the values in the histogram. The first data set has duplicate values and is not sorted by age group. The second data set includes ages that are not represented in the histogram. The third data set has values for ages 6, 11, 12, 13, 14, 15, 17, and 18, but the histogram does not have bars for all those ages. (option-a)

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why are there two of these?
Answer:

53.9

Step-by-step explanation:

89% of all houses have garages and 48% have garages and pools. We try to find houses with a pool that have a garage. Let's assume that there are 100 houses in her neighborhood. then 89 of them have garages and 48 of them have garages and pools. 48 / 89 = about 0.5393. Conver this to percent and we get 53.9

The product and the quotient of the functions are as follows:

(rs)(4) =8

(r / s)(3) = 2

A function relates input and output. It relates an independent variable with a dependent variable.

Therefore, let's solve the function as follows:

r(x) = 2√x

s(x) = √x

Therefore, let's find

(rs)(4) = r(4) × s(4) = 2√4 × √4 = 4 × 2 = 8

Let's find

(r / s)(3) = r(3) / s(3) = 2√3 / √3 = 2

Therefore,

(rs)(4) =8

(r / s)(3) = 2

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Answer:

Step-by-step explanation:

Correct option is C)

Let α be the common root,

⇒α

2

+bα+c=0.....(i) and α

2

+cα+b=0.....(ii)

(i)−(ii)⇒(b−c)α+(c−b)=0⇒α=1, since b



=c

Hence from (i) or (ii), b+c+1=0

Answer:

x2 bx 1*2

Step-by-step explanation:

The three numbers in increasing order are 296. 297 and 298

Let the consecutive natural numbers be;

first number  = x

second number = x + 1

Third number = x + 2

Now, substitute the values, we get;

x + x + 1 + x + 2 = 891

collect the like terms

x + x + x = 891 - 3

Add or subtract the like terms, we get;

3x = 888

Divide the value by the coefficient of x, we get;

3x/3 = 888/3

Divide the values

x = 296

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Answer:

- 3/4

Step-by-step explanation:

-2 1/2 - (-1 3/4)

Subtracting a negative is like adding

-2 1/2 + (1 3/4)

Get a common denominator of 4

-2 2/4 + 1 3/4

The signs are different so we subtract and take the sign of the larger

2 2/4 - 1  3/4

Borrowing from the 2

1 4/4 + 2/4 - 1 3/4

1 6/4 - 1 3/4

3/4

2 2/4 was larger and it was negative so we add a negative sign

- 3/4

The value of the expression 16/2 + 6 (7 + 4 x 5) will be 848.

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.

In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

The value of the expression 16/2 + 6 (7 + 4 x 5) will be:

= 16/2 + 6 (7 + 4 x 5)

= 8 + 6(7 + 20)

= 8 + 6(140)

= 8 + 840

= 848

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Answer: y = 1/2 or y = -1/2

Step-by-step explanation:

First move the 1 to the side with the 0

-4y^2 = -1 // -1 because when you move a number to the other side of the equation  you have to multiply -1

Then divide by -4 on each side

y^2 = 1/4

square root each side

|y| = 1/2 // sq rt y^2 becomes an absolute value because when you square root a square it automatically becomes an absolute value

so the answer would be y = 1/2 or -1/2

to check just put it into the equation as y. Both work.

EXPLANATION:

 \(1-4y^2=0\\1^2-(2y)^2=0\\(1-2y)(1+2y)=0\\\)

⇒  \(1-2y=0\)   or   \(1+2y=0\\\)

⇒ \(2y=1\)  or   \(2y=-1\\\)

⇒ \(y= \frac{1}{2}\)  or  \(y=\frac{-1}{2}\)

P/s:   \(A^2-B^2=(A-B)(A+B)\)

Ok done. Thank to me :>