Which of the following expressions cannot be factored? Explain.
a. 6 + 3x
b. 7x + 3
c. 15x + 10
d. 30x + 40

The width of the rectangle whose perimeter is 37 cm is 6.25 cm.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

The length of a rectangle is 6 cm more than its width, w cm.

So, the length = w + 6

The perimeter of the rectangle is 37 cm.

Then, Perimeter of the rectangle = 37

2(l+ w) = 37

2( w+ 6 +w )= 37

2(2w + 6)= 37

4w + 12 = 37

4w = 25

w = 6.25 cm

and, length = w+ 6 = 6 + 6.25 = 12.25 cm

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Substituting y=3 in 4x-5y=-12 we get:

Simplifying the above equation we get:

Adding 15 to the above equation we get:

Finally, dividing the above equation by 4 we get:

Answer: If 4x-5y=-12 and y=3 then:

Answer:

If the square end is under water: 312271.92  N

If the round end is under water:   262976.67 N

Step-by-step explanation:

We have to:

P = ρ·g·d

where:

P is hydrostatic pressure, g is gravitational acceleration, d is depth, ρ is fluid density

Force = hydrostatic pressure x submerged area

F = PA

You didn't specify the orientation

If the square end is under water:

F = (1000 kg/m³) (9.81 m/s²) (2) ∫ (2-y)√(64 - y²) dy .... from 0 to 2

F = 19620 ∫ (2-y)√(64 - y²) dy .... from 0 to 2

The result of the solution of the integral is 15.916

Thus:

F = 15.916*19620 = 312271.92  N

If the round end is under water:

F = (1000 kg/m³) (9.81 m/s²) (2) ∫ (y - 3) √(64- y²) dy .... from 3 to 5

F = 19620 ∫ (y - 3) √(25 - y²) dy .... from 3 to 5

The result of the solution of the integral is 13.403

Thus:

= 13.403*19620 = 262976.67 N

The hydrostatic force against one side of the plate:

If the square end is under water is 312271.92  N

If the round end is under water is 262976.67 N

This is the resultant force caused by the pressure loading of a liquid acting on submerged surfaces.

Hydrostatic pressure (P) = ρ·g·d where ρ is fluid density , g is gravitational acceleration, d is depth.

Force = hydrostatic pressure x submerged area

F = (1000 kg/m³) (9.81 m/s²) (2) ∫ (2-y)√(64 - y²) dy .. from 0 to 2

F = 19620 ∫ (2-y)√(64 - y²) dy .... from 0 to 2

 = 15.916

F = 15.916× 19620 = 312271.92  N

F = (1000 kg/m³) (9.81 m/s²) (2) ∫ (y - 3) √(64- y²) dy ... from 3 to 5

F = 19620 ∫ (y - 3) √(25 - y²) dy ...from 3 to 5

  = 13.403

F = 13.403*19620 = 262976.67 N.

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Answer:

Hope this helps

Step-by-step explanation:

4. 10^2

5. 64 / 14 * 9 + 8

64/126+8

8 64/126

8 4/9

6.   1.762 x 10^3

Answer:

I am confused with #5 but the rest are solid and checked

Step-by-step explanation:

#4 (A)

10*10=100

#5 (97)

64+4*4+3*3+2*2*2=

64+16+9+8=97

#6 (1.762 × 103)

#7 1070

Step-by-step explanation:

f(x) = mx + b, where m is the slope and b is the y-intercept

You are given m = 4.44 (lb/in^2) for every 10 ft of descent, but you want f(x) to be a function of the depth in inches, so you must find what m is for every inch of descent.  

10 ft *(12 in/ft) = 120 inches

So m = 4.44 every 120 inches of descent, therefore

m = 4.44 / 120 = 0.037 every inch of descent

So f(x) = 0.037x + b

To find b, use the fact that f(0) = 15, thus b = 15

So the equation is f(x) = 0.037x + 15

To find when the pressure is 120, set f(x) = 120 and solve for x

120 = 0.037x + 15

0.037x = 105

x = 105 / 0.037 = 2837.8 inches, which is about 236.5 ft

Answer:

\(F = 27N\)

Step-by-step explanation:

Given

Force directly proportional to acceleration

Force = 21N when Acceleraion = 7m/s^2

Required

Determine the force when acceleration = 9m/s^2

The variation between force (F) and acceleration (A) implies that:

\(F\ \alpha\ \ A\)

Convert to an equation

\(F = mA\)

Where m is constant.

When F = 21 and A = 7, we have:

\(21 = m * 7\)

Solve for m

\(m = \frac{21}{7}\)

\(m = 3\)

When A = 9

Substitute 9 for A and 3 for m in \(F = mA\)

\(F = 3 * 9\)

\(F = 27N\)

According to the equation the given all necessary math work are:

\(A: (x -f)^2 +(y -g)^2 = h^2\)

B:  domain: [-5, 11]; range: [-9, 7]

C:  yes, inside

The hypοtenuse's square is equal tο the sum οf the squares οf the οther twο sides if a triangle has a straight angle (90 degrees), accοrding tο the Pythagοras theοrem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this. Base AB, height AC, and hypοtenuse BC are all used in this equatiοn. The lοngest side οf a right-angled triangle is its hypοtenuse, it shοuld be emphasized.

Part A:

Use οf the Pythagοrean theοrem gets yοu tο the equatiοn fοr a circle in essentially οne step:

sum οf squares οf sides = square οf hypοtenuse

\((x -f)^2 +(y -g)^2 = h^2\) . . . . . . circle cantered οn (f, g) with radius h

Part B:

The circle will be defined fοr values οf x in the dοmain f ± h, and fοr values οf y in the range g ± h.

dοmain: 3 ± 8 = [-5, 11]

range: -1 ±8 = [-9, 7]

Part C:

The distance frοm pοint (10, -4) tο (f, g) is ...

\(h^2 = (10 -3)^2 +(-4 -(-1))^2\)

\(h^2 = 7^2 +(-3)^2 = 49 +9 = 58\)

h = √58 < 8 . . . . the distance tο the pοint is less than h=8.

The pοint is inside the circle.

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Hello!

We will go tu use the pythagorean theorem!

So:

BA² = BC² + AC²

AC² = BA² - BC²

AC² = 52² - 20²

AC² = 2304

AC = √2304

AC = 48

Answer:

b

Step-by-step explanation:

4.2 x 1.6=6.72

Next time if you want, use the calculator

1) For the following set of test scores for a history class, 100, 45, 60, 60, 50, 50, 45, 95, 60, 55, 40, it would be better for the teacher to consider D) The mean because it is higher and the teacher wants to feel good about the students.

2) The mode of these data about the high temperatures in Orlando for the past 8 days would be 90.

3) The median of these data about the high temperatures in Orlando for the past  8 days would be 80.

The mean, mode, and median are three centers of measurement.

The mean refers to the average value in the data set, obtained as the quotient of the total value divided by the number of items.

The mode refers to the value that occurs most in the data set.

Lastly, the median is the middle value for a data set arranged in descending or ascending order.

1. Test Scores:

100, 45, 60, 60, 50, 50, 45, 95, 60, 55, 40

Total value = 660

Number of data items = 11

Mean = 60 (660 ÷ 11)

Median = 55

Mode = 60

2. High Temperature:

91, 90, 90, 90, 84, 82, 81, 90

Total Value = 698

Number of data items = 8

Mean = (87.25 (698 ÷ 8)

Median = 90

Mode = 90

3. High Temperature:

91, 90, 90, 90, 84, 82, 81,90

Median = 80 (81, 82, 84, 90, 90, 90, 90, 91)

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According to this inequality, the number of persons attending a theatrical inequality  play, denoted by p, must be less than or equal to 275 in order for everyone to have a seat.

In mathematics, an inequality is a non-equal connection between two expressions or values. As a result, imbalance leads to inequity. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two values are not equal, the not equal symbol is typically used (). Various disparities, no matter how little or huge, are utilised to contrast values. We resuming our current status quo. Yet a variety of things lead to inequality: Negative values on both sides are split or added.

a. The disparity in representing the voting age in the United States is as follows:

a ≥ 18

In order to be eligible to vote, a voter's age, denoted by a, must be more than or equal to 18 years old.

b. The inequality used to depict a theater's seating capacity is:

p ≤ 275

According to this inequality, the number of persons attending a theatrical play, denoted by p, must be less than or equal to 275 in order for everyone to have a seat.

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f EB = 6.2, CD = 3.3, and ED= 6.2, then the value of B is 6.6.

An isosceles triangle is a type of triangle with two sides of equal  length. Two opposite angles of an isosceles triangle with equal sides are equal in size. In geometry, a triangle is a three-sided polygon that is classified into three categories based on its sides, for example:

Properties of an isosceles triangle

Therefore,

EB = 6.2

ED = 6.2

So EB=ED

ΔEBD is  isosceles triangle and ∠BCE is right angle

so C is middle point of BD

Hence, BD = 2CD

                  = 2X 3.3

                  = 6.6

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The question that is a statistical question is "How many miles did your family drive last week?"

A statistical question is a question that requires collecting and analyzing data to answer.

It involves investigating a specific variable or variables and determining patterns, trends, or relationships within the data.

The question "How many miles did your family drive last week?" is statistical, as it involves collecting and analyzing data related to a specific variable (miles driven) over a certain period of time (last week).

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Answer:

NO

Step-by-step explanation:

Answer:

Step-by-step explanation:

a) Let's denote the number of coffees sold as 'x' and the number of cappuccinos sold as 'y'.

The equation that represents the given information is:

2.50x + 3.75y = 222.50

b) To solve the equation, we need to find the values of 'x' and 'y' that satisfy the equation.

Since we have two variables and only one equation, we cannot determine the exact values of 'x' and 'y' independently. However, we can find possible combinations that satisfy the equation.

Let's proceed by assuming values for one of the variables and solving for the other. For example, let's assume 'x' is 40 (number of coffees):

2.50(40) + 3.75y = 222.50

100 + 3.75y = 222.50

3.75y = 222.50 - 100

3.75y = 122.50

y = 122.50 / 3.75

y ≈ 32.67

In this case, assuming 40 coffees were sold, we get approximately 32.67 cappuccinos.

We can also assume different values for 'x' and solve for 'y' to find other possible combinations. However, keep in mind that the number of drinks sold should be a whole number since it cannot be fractional.

Therefore, one possible combination could be around 40 coffees and 33 cappuccinos sold.

Answer:

\(\sqrt{-20}=2 \sqrt{5}\;i\)

Step-by-step explanation:

The imaginary unit is denoted by the letter \(i\) and is defined as the square root of -1:

\(\boxed{i=\sqrt{-1}}\)

To simplify the square root of -20, first rewrite -20 as the product of -1 and 20:

\(\sqrt{-20}=\sqrt{-1 \cdot 20}\)

Now rewrite 20 as the product of prime numbers:

\(\sqrt{-20}=\sqrt{-1 \cdot 2^2 \cdot 5}\)

\(\textsf{Apply the radical rule:} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}\)

\(\sqrt{-20}=\sqrt{-1} \sqrt{2^2} \sqrt{5}\)

\(\textsf{Apply the radical rule:} \quad \sqrt{a^2}=a, \quad a \geq 0\)

\(\sqrt{-20}=\sqrt{-1} \cdot 2 \sqrt{5}\)

\(\textsf{Finally, apply}\;\;\sqrt{-1}=i\)

\(\sqrt{-20}=i\cdot 2 \sqrt{5}\)

\(\sqrt{-20}=2 \sqrt{5}\;i\)

Answer:

10 weeks

Step-by-step explanation: 100÷10=10

big brain

Answer:

9 week and 4 days

Step-by-step explanation:

Answer:

7 > 24/4

Step-by-step explanation:

7 _ 24/4

Simplify 24/4

24/4 = 6

7 is greater than 6

7 > 24/4

7 is greater than the fraction 24/4 so we use the ">" symbol between them. Hence, the complete equation is 7 > 24/4.

Comparison of two numbers involves determining the relationship between them. Here are a few possible outcomes when comparing two numbers:

1: If the first number is greater than the second number, we can say that the first number is "greater than" or "larger than" the second number.

2: If the first number is less than the second number, we can say that the first number is "smaller than" or "less than" the second number.

3: If the first number is equal to the second number, we can say that the numbers are "equal" to each other.

The given numbers are:

7 and 24/4

To compare these numbers,

Convert the fraction 24/4 into the simplest form

Therefore,

\(\frac{24}{4} = 6\)

Now since 7 is greater than 6 so we use ">" between them.

Hence,

The complete equation will be 7 > 24/4.

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Answer: A

Step-by-step explanation:

\(\frac{6.3\cdot \:10^8}{9\cdot \:10^2}\)

\(=\frac{6.3\cdot \:10^6}{9}\) --> Exponent rule for division, 10^8/10^2 = 10^6

= 700,000 --> In scientific notation, 7.0×10^5

Answer:

The answer is "Initial value".

Step-by-step explanation:

The initial function value was its feature desired output unless the input signal is 0. It's an input valuing name, as well as the name for just a function's performance values set. In all input forces are defined as their function domain as well as the range of its program is called the output collection.

Answer:

initial value

Step-by-step explanation:

Answer:

The equation of the line that passes through the point (-6,8) and has a slope of -5/3 is y = (-5/3)x - 2.

Step-by-step explanation:

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

We have the point (-6,8) and a slope of -5/3.

Step 1: Use the point-slope formula to find the equation of the line in point-slope form.

y - y1 = m(x - x1)

where x1 and y1 are the coordinates of the given point.

y - 8 = (-5/3)(x - (-6))

Simplify this equation:

y - 8 = (-5/3)(x + 6)

Step 2: Convert the equation to slope-intercept form.

Distribute (-5/3) to get:

y - 8 = (-5/3)x - 10

Add 8 to both sides:

y = (-5/3)x - 2

This is the equation of the line in slope-intercept form. Therefore, the equation of the line that passes through the point (-6,8) and has a slope of -5/3 is y = (-5/3)x - 2.

Answer:

$15.48

Explanation:

100 ÷ 6.46 = 15.479876

Answer:

ujdhdbhd 828wiuwvsnzj njsjbsksbs loshsbmsks bjsbsksbsn

Answer:

A. Fractions 1 and 4

B. Fractions 1, 2, and 3

Step-by-step explanation:

A negative divided by a positive is a negative.

A positive divided by a negative is a negative.

If the negative symbol is in line with the fraction bar, it is still a negative.

Answer:

The decibel level of this second sound is 48.021 decibels.

Step-by-step explanation:

The acoustic intensity (\(B_{dB}\)), measured in decibels, is defined by the following formula:

\(B_{dB} = 10\cdot \log_{10}\left(\frac{I}{I_{o}} \right)\) (1)

Where:

\(I_{o}\) - Reference sound intensity, measured in watts per square meter.

\(I\) - Real sound intensity, measured in watts per square meter.

If we know that \(B_{dB} = 42\,dB\) and \(I_{o} = 10^{-12}\,\frac{W}{m^{2}}\), then the real sound intensity of the first sound is:

\(\frac{B_{dB}}{10} = \log_{10}\left(\frac{I}{I_{o}} \right)\)

\(\frac{I}{I_{o}} = 10^{\frac{B_{dB}}{10} }\)

\(I = I_{o}\cdot 10^{\frac{B_{dB}}{10} }\)

\(I = \left(10^{-12}\,\frac{W}{m^{2}} \right)\cdot 10^{\frac{42\,dB}{10} }\)

\(I = 1.585\times 10^{-8}\,\frac{W}{m^{2}}\)

The real sound intensity of the second sound is four times greater, that is:

\(I' = 6.340\times 10^{-8}\,\frac{W}{m^{2}}\)

If we know that \(I_{o} = 10^{-12}\,\frac{W}{m^{2}}\) and \(I' = 6.340\times 10^{-8}\,\frac{W}{m^{2}}\), then the acoustic intensity of the second sound is:

\(B_{dB} = 10\cdot \log_{10}\left(\frac{I'}{I_{o}} \right)\)

\(B_{dB} = 10\cdot \log_{10}\left(\frac{6.340\times 10^{-8}\,\frac{W}{m^{2}} }{10^{-12}\,\frac{W}{m^{2}} } \right)\)

\(B_{dB} = 48.021\,dB\)

The decibel level of this second sound is 48.021 decibels.

The domain of the function represented in the graph will be 20 ≤ x ≤ 60, or x is from 20 to 60. Then the correct option is D.

A line segment in mathematics has two different points on it that define its boundaries.

A line segment is sometimes referred to as a section of a path that joins two places.

Six-year-old students at an elementary school were given a 20-yard head start in a race. The graph shows how far the average student ran in 30 seconds.

A line graph with Distance, in yards, on the x-axis and Age of the Runner on the y-axis. The x-axis has a scale from 0 to 80 in increments of 10. The y-axis has a scale of 0 to 8 in increments of 2. A straight line connecting 20, 6, and 60, 6 is drawn.

The domain of the function represented in the graph will be 20 ≤ x ≤ 60, or x is from 20 to 60. Then the correct option is D.

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Answer:

the correct option is D

Step-by-step explanation:

Answer:

All real numbers

Step-by-step explanation:

The domain is where the graph touches all of the x-coordinates. This parabola touches all x-coordinates from -infinity to +infinity (all real numbers) because it continues outward forever.

Answer: all real numbers

Step-by-step explanation:

The domain is how many x values are possible, but there is no limit to that, it is infinite. So the domain is all real numbers.