Solve the quadratic equations in questions 1 – 5 by factoring.

1. x2 – 49 = 0

2. 3x3 – 12x = 0

3. 12x2 + 14x + 12 = 18

4. –x3 + 22x2 – 121x = 0

5. x2 – 4x = 5

Answer: The equation used to find the value of x is 5x - 4 = 3x + 10. The value of x is determined to be 7.

Step-by-step explanation:

Four less than the product of a number (x) and 5 = 5x - 4

8 more than 2 added to 3 times the number = 3x + 2 + 8 = 3x + 10

Four less than the product of a number (x) and 5 is equal to 8 more than 2 added to 3 times the number => 5x - 4 = 3x + 10

                                                         5x - 3x = 10 + 4

                                                         2x = 14

                                                         x = 14/2

                 therefore,                      x = 7

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Answer:

Below

Step-by-step explanation:

32/2 x 100% = 1600 %

The first step will be subtract 3 from each side of the model.

By subtracting 3 from each side of the model, the 3 in the Right Hand Side will be cancelled, and the model will be:

2x = 5 - 3 = 2

Then the next step will be dividing 2 from each side of the model.

2x + 3 = 5

By subtracting 3 to both the sides, we get

2x + 3 - 3 = 5 - 3

or, 2x = 2

By dividing 2 to both the sides, we get

2x/2 = 2/2

or, x = 1

The value of x is 1.

If spring A has a spring constant which is 8 times spring B's spring constant then the ratio of their periods is = 9K and  \(\frac{9K}{8}\)

Spring stiffness is a characteristic that describes the relationship between load and deflection. If k is stiffness, P is load, and x is deflection, P = kx. The smaller the deflection at a constant load, the stiffer the spring, k.

Given that,

If spring A has a spring constant which is 8 times spring B's spring constant,

Let us assume,

A spring is cut into two parts of length La and Lb

Also given that La : Lb

La : Lb = 1 : 8

The total of spring constant is = 1 + 8 = 9

If the length of spring is L , then La

La = \(\frac{L}{9}\)

And length of B , Lb

Lb = \(\frac{8L}{9}\)

We know, for spring force , spring constant or stiffness of spring is inversely proportional to length of spring .

K ∝ 1 / L

If initial spring constant is k then,

kL= KaLa = KbLb

Then,

Ka = \(\frac{K}{\frac{1}{9} }\)

Ka = 9K

And Kb = \(\frac{K}{\frac{8}{9} }\)

Kb = \(\frac{9K}{8}\)

Hence, stiffness of A is given by, 9K

Stiffness of B is given by  \(\frac{9K}{8}\)

Therefore,

If spring A has a spring constant which is 8 times spring B's spring constant then the ratio of their periods is = 9K and  \(\frac{9K}{8}\)

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The measure of the j of triangle ΔHIJ is given by the law of sine and is given by j = 2.3 inches

The relationship between a triangle's sides and angles is provided by the Law of Sines. Trigonometry's law of sines can be expressed as a/sinA = b/sinB = c/sinC, where a, b, and c are the lengths of the triangle's sides, and A, B, and C are the triangle's respective opposite angles.

Law of Sines :

a / sin A = b / sin B = c / sin C

Given data ,

Let the triangle be represented as ΔHIJ

Now , the equation will be

The measure of i = 2.8 inches

The measure of ∠I = 68°

The measure of j = j

The measure of ∠J = 50°

Now , from the law of sines , we get

a / sin A = b / sin B

Substituting the values in the equation , we get

2.8 / sin ( 68 )° = j / sin ( 50 )°

On simplifying the equation , we get

2.8 / 0.92718 = j / 0.766044

Multiply by 0.766044 on both sides of the equation , we get

j = 3.0198972 x 0.766044

On further simplification , we get

j = 2.3 inches

Hence , the measure of j of triangle is 2.3 inches

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Answer:

2√2 units.

Step-by-step explanation:

To find the length of the line joining points A(3, 5) and B(1, 3), we can use the distance formula. The distance formula is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the coordinates of points A and B into the formula, we have:

d = sqrt((1 - 3)^2 + (3 - 5)^2)

  = sqrt((-2)^2 + (-2)^2)

  = sqrt(4 + 4)

  = sqrt(8)

  = 2sqrt(2)

Therefore, the length of the line joining points A and B is 2√2 units.

The answer is explained below.

In order to be considered a language, a system of communication must have vocabulary, grammar, syntax, and people who use and understand it. Mathematics meets this definition of a language. Linguists who don't consider math a language cite its use as a written rather than spoken form of communication.

Mathematics is pure language - the language of science. It is unique among languages in its ability to provide precise expression for every thought or concept that can be formulated in its terms. In a spoken language, there exist words, like "happiness", that defy definition.

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Answer:

y = x - 1

Step-by-step explanation:

That's correct. The rate in the portion formula can be expressed as a decimal, fraction, or percentage, depending on the context and what is most convenient for the problem being solved.

How do you calculate ratio and proportion? Ans: The ratio formula is written as a: b a/b for any two numbers. Contrarily, the percentage formula is written as a:b::c:da:b::c:da:b=cd.

An equation in which two ratios are made equal is known as a percentage. As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls) 1 out of 4 are boys, and 3/ 4 are girls.

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The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

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Answer:

Option A = 6

Step-by-step explanation:

3x- 5 = x+ 7           ( as diagonals r equal in a recangle)

3x-x = 7+ 5

2x = 12

x = 12/ 2 = 6

I hope im  Right !!

Answer:

1. 2.5 ft

2. Yes

3. Yes

Step-by-step explanation:

Theorem:

A segment whose endpoints are the midpoints of two sides of a triangle is parallel to and half the length of the third side.

Let's think of this theorem as it applies to our triangle.

We have triangle GIS. The endpoints of segment WN are the midpoints of sides IS and IG. Therefore, by the theorem above, segment WN is parallel to side SG and half the length of segment SG.

1. W is the midpoint of IS.

IW = WS = (1/2)SI

SI = 5 ft

WS = (1/2)SI = (1/2) × 5 ft = 2.5 ft

Answer: 2.5 ft

2. From the theorem, WN = (1/2)SG

SG = 5 ft

WN = (1/2) × 5 ft = 2.5 ft = 2.5 ft × (12 in.)/(1 ft) = 30 in.

A 36 in. long piece is long enough since WN is only 30 in.

Answer: Yes

3. Yes by the theorem above.

Answer: Yes

Random variation in a process indicates natural variation ; whereas non-random variation indicates process variation

Random variation in a process refers to the natural variation or randomness that occurs in a process due to various factors that are not controlled or predictable. For example, in a manufacturing process, random variation can be caused by factors such as differences in raw materials, operator error, or environmental conditions that are not controlled.

On the other hand, non-random variation in a process refers to the variation that is not due to chance and is likely caused by specific factors that are affecting the process. Non-random variation is also known as special cause variation. Special cause variation can be caused by factors such as a change in machine settings, a change in process parameters, or a change in the process inputs.

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Based on the supply graph and demand graph shown above, the price at the point of equilibrium is $ 30.

Demand refers to quantity of a commodity that the consumers are willing to, able to purchase at a given price during a given period of time. Supply refers to quantity of a commodity that the producers are willing to, able to offer for sale at a given price during a given period of time.

Demand curve slopes downward due to inverse relationship between price and quantity demanded whereas supply curve slopes upward due to direct relationship between quantity supplied and price. When both demand and supply curve intersect with each other balance is achieved. Intersection point between demand and supply curve is known as equilibrium.

At this point when prices are equal is known as equilibrium price and when quantiy demanded or supplied are equal it is known as equilibrium quantity. When we combine the given graph. Equilibrium is achieved at a point when price is equal to $ 30 and quantity is equal to 20 units.

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The Greatest Common Divisor (GCD) of 85 and 51 is 17.

The greatest common factor that divides two or more numbers is known as the greatest common divisor (GCD). The highest common factor is another name for it (HCF).

Explanation

Step 1: Divide 85 by 51. The quotient is 1 and the remainder is 34.

Step 2: Divide 51 by 34. The quotient is 1 and the remainder is 17.

Step 3: Divide 34 by 17. The quotient is 2 and the remainder is 0.

Step 4: Since the remainder is 0, the Greatest Common Divisor (GCD) of 85 and 51 is 17.

The GCD of 85 and 51 is 17.

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The equation for the proportion, p, of consumers who shop with coupons is: p = C/N where C is the number of consumers who use coupons and N is the total number of consumers asked.

An equation is a mathematical statement that indicates the equality of two expressions. It consists of two expressions separated by an equal sign (=). The expression on the left side of the equal sign is equivalent to the expression on the right side. Equations can have one or more variables, which are usually represented by letters such as x, y, or z. The goal in solving an equation is to determine the value(s) of the variable(s) that make the equation true. This involves manipulating the expressions on both sides of the equal sign using algebraic operations such as addition, subtraction, multiplication, and division, to isolate the variable on one side of the equation. Equations are used in many areas of mathematics and science to represent relationships between variables and to solve problems. They are also used in various fields such as engineering, physics, and economics to model real-world situations and make predictions based on mathematical analysis.

Here,

This equation represents the ratio of the number of consumers who use coupons to the total number of consumers. It is commonly used in statistics and market research to measure the prevalence of a certain behavior or preference among a population. By calculating the proportion of consumers who use coupons, businesses can make informed decisions about their pricing strategies, promotions, and advertising campaigns.

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Answer:

The GCD of 510 and 92 is 2

Step-by-step explanation:

510 : 2 = 255

510 : 3 = 170

510 : 4 = 127.5

92 : 2 = 46

92 : 3 = 30.6667

92 : 4 = 23

hope this helps!

Answer:

ion know Maybe....6,6,8

Step-by-step explanation:

hope it correct tho

Therefore, the gas temperature can be raised by 1093.4 times the original temperature (25ºC) without breaking the container, as long as the volume of the container remains constant.

Multiplication is a mathematical operation where two or more numbers are combined to give a result called the product. It is represented by the multiplication sign "×" or the dot "."

Here,

To determine how much the gas temperature can be raised without breaking the container, we can use the ideal gas law:

PV = nRT

where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the absolute temperature.

Assuming that the volume of the container is constant, we can rearrange the ideal gas law to solve for the temperature:

T = (P * V) / (n * R)

Since the amount of gas (n) and the volume (V) are constant, we can simplify the equation to:

T = (P / R) * (constant)

where the constant is the ratio of the volume and the amount of gas (V/n).

Now, we can use the given values to find the initial temperature of the gas:

T1 = (0.8 atm / R) * (constant)

Next, we can use the maximum pressure that the container can withstand to find the maximum temperature of the gas:

T2 = (2.0 atm / R) * (constant)

The temperature difference between T1 and T2 represents how much the gas temperature can be raised without breaking the container:

ΔT = T2 - T1 = [(2.0 atm / R) * (constant)] - [(0.8 atm / R) * (constant)]

ΔT = (1.2 atm / R) * (constant)

Since the volume of the container is constant and the amount of gas is fixed, the constant in the equation is the same for both T1 and T2, and therefore cancels out when we calculate the temperature difference.

Thus, we can simplify the equation to:

ΔT = (1.2 atm / R) * (V/n)

Using the ideal gas law equation and plugging in the given values, we get:

P1V1/T1 = P2V2/T2

Solving for T2, we get:

T2 = (P2/P1) * (V1/T1) * T1

Substituting the given values, we get:

T2 = (2 atm / 0.8 atm) * (V1 / (25 + 273.15) K) * (25 + 273.15) K

Simplifying the expression, we get:

T2 = 1093.4 * V1

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Complete question:

A certain amount of gas is contained in a glass container at 25ºC and a pressure of 0.8 atm. Suppose the container can withstand a maximum pressure of 2.0 atm. How much can the gas temperature be raised without breaking the container?

Answer:

3 red golf balls

Step-by-step explanation:

There are 2 red golf balls and 6 other golf balls, so there is a total of 8 golf balls. 6 + 2 = 8

Now find the probability of selecting a red golf ball

(p of red) = 2/8

reduce

(p of red) = 1/4

Now multiply the probability by 12 to how many you expect to be red.

1/4 x 12/1

12/4 = 3

3 red golf balls

Answer:

  y -5 = -4(x -5)

Step-by-step explanation:

You want the line through (5, 5) that is perpendicular to one with slope 1/4.

Perpendicular lines have slopes that are the opposite reciprocals of one another. Your desired line has slope ...

  m = -1/(1/4) = -4

The point-slope equation of a line with slope m through point (h, k) is ...

  y -k = m(x -h)

For your line, you have m = -4, (h, k) = (5, 5), so the equation is ...

  y -5 = -4(x -5)

Answer:GIVE A BETTER DETAILED QUESTION sorry for caps

Step-by-step explanation:

Answer:

72

Step-by-step explanation:

4+6+6+2=18

and u added 4 numbers so 18×4=72

Answer:d and a

Step-by-step explanation:

Answer:

It is not a integer, it is a rational number

Answer: No, this isn't. An integer is any whole number, positive or negative. Having extraneous digits to the right of the decimal other than zero, radicals or any fractions are excluded from being considered an integer. Integers, for example, are 2, 85, -923, etc. Hope this helps!

Step-by-step explanation:

The number of gallons that would be saved after the recycling 4 tons of paper would be 27, 812

Proportion can be defined as the mathematical comparison of two numbers.

It is also said to be an equation defining two given ratios as equivalent to each other.

From the information, we have that;

By recycling 1 ton of paper, 6, 953 gallons of water was saved

To determine the gallons of water that would be saved after recycling 4 tons of paper, we have to;

If 1 ton of paper = 6, 953 gallons of water

Then 4 tons of paper = x

cross multiply

x × 1 = 6953 × 4

multiply through

x = 27, 812 gallons

The number of gallons that would be saved after the recycling would be

27, 812 gallons

Thus, the number of gallons that would be saved after the recycling 4 tons of paper would be 27, 812

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Answer:Her friend is right Danielle needs to work for 5 hours

Step-by-step explanation:

hope this help

The three points which are a solution to the equation are:

(-4,1) , (-6,5) and (-3,-1)

Given:

2x+y=-8

Solving (a): The possible coordinates.

we have:

(x,y) = (-7,-3)

⇒ 2x+y=-7

⇒ 2(-7)+(-3) = -7

⇒ -14-3 = -7

⇒-18=-7

hence (-7,-3) is not a point on the grid.

(b) (-4,1)

we have:

(x,y) = (-4,1)

⇒ 2x+y=-7

⇒ 2(-4)+(1) = -7

⇒ -8+1 = -7

⇒ -7 = -7

hence (-4,1) is a point on the grid.

(c) (-6,5)

we have:

(x,y) = (-6,5)

⇒ 2x+y=-8

⇒ 2(-6)+(5) = 8

⇒ -12+5 = -7

⇒ -7= -7

hence (-6,5) is a point on the grid.

(d) (0,3)

we have:

(x,y) = (0,3)

⇒ 2x+y=-8

⇒ 2(0)+(3) = 8

⇒ 0+3 = -7

⇒ 3= -7

hence (0,3) is not a point on the grid.

(e) (-4,6)

we have:

(x,y) = (-4,6)

⇒ 2x+y=-8

⇒ 2(-4)+(6) = 8

⇒ -8+6 = -7

⇒ -2= -7

hence (-4,6) is not a point on the grid.

(f) (-3,-1)

we have:

(x,y) = (-6,5)

⇒ 2x+y=-8

⇒ 2(-3)+(-1) = -7

⇒ -6-1= -7

⇒ -7= -7

hence (-3,-1) is a point on the grid.

The three points on the grid are:

(-4,1) , (-6,5) and (-3,-1) are the points on the grid.

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