a rectangle has a length that is 5 inches greater than its width, and its area is 104 square inches. The equation(x+5) x=104 represents the situation, where x represents the width of the rectangle. (x+5) x=104 x2+5x-104=0. Determine the solutions of the equation. What solution makes sense for the situation?

Answer:

it can and cant at the same time.

The expression 126 \(m^4\) - 63\(m^3\) is equivalent to the given expression                  7m² * (2m -1 )*(m9).

The properties of multiplication are:

There are different power rules, see some them:

1. Multiplication with the same base: you should repeat the base and  add the exponents.

2. Division with the same base: you should repeat the base and  subctract the exponents.

3.Power. For this rule, you should repeat the base and multiply the exponents.

4. Zero Exponent. When you have an exponent equals to zero, the result must be 1.

Here, you should apply the distributive property and power rules for solving this expression and finding an equivalent expression.

First, you should multiply the factors (2m -1)*(9m). As result, you find 18m²-9m.

After that, you should do the product between the previous result (18m²-9m) and the factor 7m². Thus,

(18m²-9m) * 7m²= 126 \(m^4\) - 63\(m^3\).

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One way to simplify variables with many levels (or decimal places) when creating a frequency distribution is to organize the data into class intervals (option B).

By grouping the data into intervals, the frequency distribution becomes more manageable and easier to interpret. This process involves dividing the range of values into distinct intervals or categories and then counting the number of observations falling within each interval. Class intervals provide a summary of the data by grouping similar values together, reducing the complexity of individual levels or decimal places.

This simplification technique is particularly useful when dealing with large datasets or continuous variables that have numerous levels or decimal values, allowing for a clearer representation and analysis of the data.

Option B holds true.

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Answer:

-1280

Step-by-step explanation:

10×(-2)= -20

-20×(-2)= 40

4th term: 40×(-2)= -80

5th term: -80×(-2)= 160

6th term: 160×(-2)= -320

7th term: -320×(-2)= 640

8th term: 640×(-2)= -1280

The point, M, that is midway between P=(5,−8,−6) and Q=(-7,-2,-8) is

In geometry, the midpoint formula is an equation that determines the separation between two known coordinate locations at their halfway point.

The midway between the points P and Q is calculated using the method

Mid point = ((x₁ + x₂)/2, (y₁ + y₂)/2, (z₁ + z₂)/2)

Applying the method to the given points gives

P = (5, −8, −6) and Q = (-7, -2, -8)

M = ((5 + -7)/2, (-8 + -2)/2, (-6 + -8)/2)

M = (-1, -5, -7)

The coordinates of point M (-1, -5, -7) is the mid way between point  P=(5,−8,−6) and Q=(-7,-2,-8).

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The term for the value that occurs most often in a series of numbers is called the mode.

The mode is one of the three main measures of central tendency, along with the mean and the median. It is a useful descriptive statistic that can provide insights into the characteristics of a dataset.

To find the mode of a set of data, you first need to arrange the data in order, either in increasing or decreasing order. Then, you simply identify the most frequent data point, which is the mode. In some cases, there may be more than one mode if multiple data points occur with the same maximum frequency.

The mode is particularly useful when dealing with categorical or nominal data, where there are distinct categories or values that cannot be ordered in a meaningful way. For example, the mode can help identify the most popular color among a group of people or the most common type of car on a given street. It can also be used for continuous data, although it may be less useful in this case than the mean or median.

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3:5

Step-by-step explanation:

change the kilogram into gram and then divide it

Answer:

3 : 5

Step-by-step explanation:

The quantities must have the same units

1 Kg = 1000 g , then

600 : 1000 ( divide both parts by 200 )

= 3 : 5 ← in simplest form

Answer:

2

Step-by-step explanation:

2⁹ ÷ (4^x) = 32^x × 32^(-1)

2⁹ ÷ 32^(-1) = 32^x × 4^x

16384 = 128^x

Kalau kamu dah belajar logaritma,

\(x = log_{128}(16384) \\ x = 2\)

Jika belum,

2¹⁴ = 2^(7x)

Bandingkan kuasa persamaan tersebut,

7x = 14

x = 2

The solution of the given question is as follows :A club is choosing 2 members to serve on a committee.

Based on chance alone, the probability that one woman and one man will be chosen to be on the committee are as follows :Probability of selecting 1 woman out of 3 = 3C1 = 3Probability of selecting 1 man out of 1 = 1C1 = 1Probability of selecting 2 members from 4 = 4C2 = 6Therefore, the total number of ways that 2 members can be selected from 4 are: 3 × 1 × 6 = 18There are 18 different possible ways that a committee can be formed consisting of one woman and one man out of 3 women and 1 man.

Thus, the probability that one woman and one man will be chosen to be on the committee is: 3 × 1/6 = 1/2.00 = 0.5000 the probability that one woman and one man will be chosen to be on the committee is 0.5000 or 50% or 1/2 (in fraction) or 0.5 (in decimal).Hence, the solution of the given question is as follows: Probability that one woman and one man will be chosen to be on the committee is 0.5000.

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Answer:

Slope: 3

Equation: y + 2 = 3(x + 1)

Step-by-step explanation:

Find the slope using (-1, -2) and (0, 1):

\( slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - (-2)}{0 - (-1)} = \frac{3}{1} = 3 \)

Slope (m) = 3

The equation can be represented in point-slope form, y - b = m(x - a)

Where,

(-1, -2) = (a, b)

m = 3

Plug in the values into y - b = m(x - a)

y - (-2) = 3(x - (-1))

y + 2 = 3(x + 1)

Answer:

There is a 40% probability of Jonah grabbing  a powdered doughnut from  Bag 1.

Step-by-step explanation:

Total number of doughnuts in the bag 1 =20

Total powdered doughnuts in each bag = 8

Probability of selecting powdered doughnut from  Bag 1 by Jonah =

\(\frac{8}{20} * 100\\40\)%

Answer:

\( {3}^{2h - 1} = {3}^{6} \times {3}^{3} \\ {3}^{2h - 1} = {3}^{9} \\ so...... \\ 2h - 1 = 9 \\ 2h = 10 \\ h = \frac{10}{2} = 5\)

Answer:

Nope

Step-by-step explanation:

If you distribute the 3/4a they are no where near equal

The number of students should we survey is 136.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

To estimate the required sample size for estimating the proportion of students with tattoos with 98% confidence and a margin of error of no more than 0.10, we can use the formula:

n = (z² × p × (1-p)) / (E²)

where:

n = sample size

z = z-score associated with the desired confidence level (98% = 2.33)

p = estimated proportion of students with tattoos (unknown)

E = margin of error (0.10)

We don't know the value of p, but since we want the maximum possible sample size

Let us assume that p = 0.5, which gives us the largest possible value of n.

So, substituting the values into the formula, we get:

n = (2.33² × 0.5×(1-0.5)) / (0.10²) = 135.7

Hence, the number of students should we survey is 136.

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Answer:

a

Step-by-step explanation:

in y intercept x = 0 so the choice a become the answer

To find the least-squares solution x* of the system, we need to solve the equation Ax = b, where A is the coefficient matrix, x is the vector of unknowns, and b is the vector of constants. x₁ = -6 and x₂ = 1.

The given system can be written as:

[1 0]   [x₁]   [-6]

[0 1] * [x₂] = [ 1]

[0 0]   [x₃]   [-3]

Since the third row of the coefficient matrix is all zeros, it does not contribute to the equation. Therefore, we can ignore it for the purpose of finding the least-squares solution.

The reduced system becomes:

[1 0]   [x₁]   [-6]

[0 1] * [x₂] = [ 1]

This simplified system is already in the form of Ax = b, where A is the 2x2 identity matrix and b is the given vector. So the least-squares solution x* is simply equal to the vector b.

Therefore, the least-squares solution x* is:

x* = [-6]

      [ 1]

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The maximum burn rate ∣ΔM/Δt∣ that the engine could reach before the ship's acceleration exceeded 5 g and its human occupants began to lose consciousness is approximately 51.0 kg/s.

Acceleration is directly proportional to the force acting on an object. In simple terms, if the force on an object is greater, then it will undergo more acceleration. However, there are limitations to the acceleration that can be tolerated by the human body. At about 5 g (49.0 m/s2) for more than a few seconds, an average person starts to lose consciousness. Let's use this information to answer the given question.

Let the maximum burn rate |ΔM/Δt| that the engine could reach before the ship's acceleration exceeded 5 g be x.

Let the mass of the spaceship be m and the exhaust speed of the engine be v.

Using the formula for the thrust of a rocket,

T = (mv)e

After substituting the given values into the formula for thrust, we get:

T = (3.00 × 104)(2.50 × 103) = 7.50 × 107 N

Therefore, the acceleration produced by the engine, a is given by the formula below:

F = ma

Therefore,

a = F/m= 7.50 × 107/3.00 × 104= 2.50 × 103 m/s²

The maximum burn rate that the engine could reach before the ship's acceleration exceeded 5 g is equal to the acceleration that would be produced by a maximum burn rate. Therefore,

x = a/5g= 2.50 × 103/(5 × 9.8)≈ 51.0 kg/s

Therefore, the maximum burn rate ∣ΔM/Δt∣ that the engine could reach before the ship's acceleration exceeded 5 g and its human occupants began to lose consciousness is approximately 51.0 kg/s.

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The required explicit formula for the given sequence to determine the nth term is given as nth term = 8 + (n - 1)3.

Arithmetic progression is the series of numbers that have common differences between adjacent values.

here,
The Sequences 8, 11, 14,...

first term a = 8
common difference = 11 - 8 = 3

Now,
The explicit formula is given as,
nth terms = a + (n - 1)d
nth term = 8 + (n - 1)3

Thus, the required explicit formula for the given sequence to determine the nth term is given as nth term = 8 + (n - 1)3.

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2 miles per minute. Dang, that's one fast guy.

Answer:

x4-x3-2x2-4x+12

Step-by-step explanation:

(f-g)(x)=f(x)-g(x)

=> x4-4x2+4-(x3-2x2+4x-8)

=> x4-4x2+4-x3+2x2-4x+8

=> x4-x3-2x2-4x+12

The value of the function (f-g)(x) is \(x^4-x^3-2x^2-4x+12\).

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given functions are \(f(x)=x^4-4x^2+4\) and g(x)=x³-2x²+4x-8.

Now, (f-g)(x)=f(x)-g(x)

= (\(x^4-4x^2+4\))-(x³-2x²+4x-8)

= \(x^4-4x^2+4\)-x³+2x²-4x+8

= \(x^4-x^3-2x^2-4x+12\)

Therefore, the value of the function (f-g)(x) is \(x^4-x^3-2x^2-4x+12\).

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The speed of the light in miles per hour is

66913574.4 miles per hour

It is the conversion of one unit to another unit with its standard conversion.

Example:

1 minute = 60 seconds

1 km = 1000 m

1 hour = 60 minutes

We have,

1 km = 0.62 mi

1 min = 60 s

1 hr = 60 min

Speed of light = 299,792 km per second

This can be written as,

1 km = 0.62 miles

299792 km = 299792 x 0.62 miles

299792 km = 185871.04 miles

1 hour = 60 minute

1 hour = 360 seconds

1/360 hour = 1 second

1 second = 1/360 hour

Now,

= 299792 km / 1 second

= 185871.04 miles / 1/360 hour

= 185871..04 x 360 miles per hour

= 66913574.4 miles per hour

Thus,

The speed of the light is 66913574.4 miles per hour.

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Here, we want to use the imaginary number to rewrite the given expression as a complex number

Mathematically, the complex number can be written as;

Thus, we have;

Step-by-step explanation:

\( \frac{4}{3} \pi {(4.3)}^{3} \\ \frac{4}{3} \pi(79.507) \\ \frac{318.028}{3} \pi \\ 106.0093\pi \\ \frac{1}{2} 333.038 \\ 166.5 {cm}^{3} \)

Answer:A

Step-by-step explanation:

20/25 = 4/5

16/20 = 8/10 = 4/5

The equation of the line in slope intercept form is y = (-4/3)x   .

In the question ,

a line graph is given ,

we need to find the equation of that line .

the two points that are given on the line graph are (-3 , 4) and (0 , 0) ,

the equation of the line passing from the points (x₁ , y₁) with slope m  in the slope intercept form is given by

(y - y₁) = m(x - x₁) .

we first need to find the slope .

So , m = (0 - 4)/(0 + 3)

m = -4/3

The equation of the line passing from the points (-3 , 4) with slope -4/3 , in the slope intercept form is

(y - 4) = (-4/3)(x -(-3))

y - 4 = (-4/3)(x + 3)

y - 4 = (-4/3)x - 4

y = (-4/3)x - 4 + 4

y = (-4/3)x

Therefore , The equation of the line in slope intercept form is  y = (-4/3)x  .

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The possible approximate lengths of b are: 2.3 units and 7.8 units

We know that the law of sines for triangle is:

The ratios of the length of all sides of a triangle to the sine of the respective opposite angles are in proportion.

This means, for triangle ABC,

\(\frac{sin~ A}{a} =\frac{sin~B}{b} =\frac{sin~ C}{c}\)

where a is the length of side BC,

b is the length of side AC,

c is the length of side AB.

For triangle ABC consider an equation from sine law,

\(\frac{sin~ A}{a} =\frac{sin~ C}{c}\)

here, c = 5.4, a = 3.3, and m∠A = 20°

\(\frac{sin~ 20}{3.3} =\frac{sin~ C}{5.4}\\\\\frac{0.3420}{3.3} =\frac{sin~ C}{5.4}\)

0.3420 × 5.4 = 3.3 × sin(C)

sin(C) = 0.5596

∠C = arcsin(0.5596)

∠C = 34.03°  OR 145.9°

∠C ≈ 34° OR 146°

We know that the sum of all angles of triangle is 180 degrees.

so, ∠A + ∠B + ∠C = 180°

when m∠C = 34°,

20° + ∠B + 34.03° = 180°

∠B = 125.97°

m∠B = 126°

when m∠C = 146°,

20° + ∠B + 146° = 180°

m∠B = 14°

Now consider equation,

\(\frac{sin~ A}{a} =\frac{sin~ B}{b}\\\\\frac{sin~20^{\circ}}{3.3} =\frac{sin~ 126^{\circ}}{b}\)

b × 0.3420 = 0.8090 × 3.3

b = 7.8 units

when m∠B = 14°,

\(\frac{sin~20^{\circ}}{3.3} =\frac{sin~ 14^{\circ}}{b}\)

b × 0.3420 = 0.2419 × 3.3

b = 2.3 units

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The complete question is:

Law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction

In ΔABC, c = 5.4, a = 3.3, and measure of angle A = 20 degrees. What are the possible approximate lengths of b? Use the law of sines to find the answer.

2.0 units and 4.6 units

2.1 units and 8.7 units

2.3 units and 7.8 units

2.6 units and 6.6 units

Answer:

To obtain the third side of an isosceles triangle with two sides known, use the Pythagorean theorem if it is a right triangle or provide additional information if it is no

Step-by-step explanation:

You can follow these steps:

Identify the two sides that are known. In an isosceles triangle, these will be the two equal sides, often referred to as the legs of the triangle.

Determine the length of the base. The base is the third side of the triangle, and it is the side that is not equal to the other two sides.

If the isosceles triangle is also a right triangle, you can use the Pythagorean theorem to find the length of the base. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. So, you can use the formula:

base^2 = (leg1)^2 + (leg2)^2

Take the square root of both sides to solve for the base:

base = √((leg1)^2 + (leg2)^2)

If the isosceles triangle is not a right triangle, you need additional information to determine the length of the base. This could be the measure of an angle or another side length.

Remember that the lengths of the two equal sides (legs) in an isosceles triangle are always equal, while the length of the base is different.

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