What are the solutions of the equation 3x² – 5x + 2 = 0? U C D 1 and 2 1 and Homb -1 and -2 -1 and -2​

Answer:

3/7 meters

Step-by-step explanation:

[tex] \sqrt{ \frac{9}{49} } = \frac{ \sqrt{9} }{ \sqrt{49} } = \frac{3}{7} [/tex]

To meet the​ recommendation, the ramp needs to have a horizontal distance of at least 16 feet. The ramp has a horizontal distance of 17.9 feet.

If the ramp has a horizontal distance of 17.9 feet, it meets the recommended minimum distance of 16 feet for a ramp with a maximum slope of 1:12, as per the ADA Accessibility Guidelines.

It's important to note that the slope of the ramp should also be taken into consideration to ensure that it is safe and easy to use for individuals with disabilities. If the ramp's slope is too steep or too shallow, it may not meet accessibility standards and could pose a hazard to users.

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The system of inequalities "2x – y > 1 and x – 2y < –1." are graphically shown below in the image section.

Inequalities in mathematics describe the connection between two non-equal values. Equal does not necessarily mean unequal. When two values are not equal, we typically use the "not equal symbol ()". However, a number of inequality comparisons are made to determine whether one value is greater than or less than another. The various inequality symbols, their meanings, and methods for solving them will all be covered in this article using examples of both one- and two-variable linear inequalities. We'll also discuss the algebraic inequalities that are commonly used.

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—------ CORRECT QUESTION FORMAT IS GIVEN BELOW - - - - - -

(Q). Solve the following system of inequalities graphically: 2x – y > 1 and x – 2y < –1.

As each side of the cube has a surface area of 24in².the total amount of wrapping paper needed is 64in².

Surface area is the total area of a three-dimensional object's surface, including the area of its faces and any curved surfaces.

To calculate the amount of wrapping paper needed for the cube, we can use the formula for the surface area of a cube:

SA = 6 x (side)²

In this case, the side of the cube is 2in,

so the SA = 6 x (2in)² = 24in²

To get the amount of wrapping paper needed, we would need to multiply this by 4, as each side of the cube has a surface area of 24in².

Therefore, the total amount of wrapping paper needed is

24in² x 4 = 96in²

To convert this to a square, we would need to divide it by 4, as each side of the square is equal in length.

Therefore, the total amount of wrapping paper needed is

96in² / 4

= 24in x 4

= 64in².

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The coordinate A when the triangle is reflected over the y-axis is (2, 5)

From the triangle, we have

A = (-2, 5)

Reflecting a point over the x-axis is a type of transformation that involves flipping the point across the x-axis.

The reflection involves keeping the y-coordinate of the point the same, but changing the sign of the x-coordinate.

In this case, the original point is (-2, 5). To reflect this point over the y-axis, we keep the y-coordinate (5) the same, but change the sign of the x-coordinate to positive,

Resulting in the reflected point (2, 5).

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After answering the presented question, we can conclude that As a result, the equation of the straight line passing through (3,5) and having an x-intercept three times the y-intercept is: 5x - 9y = -42

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

To find a straight line's equation, we must first establish its slope and y-intercept.

[tex](y - 5) = m(x - 3) (x - 3)\\b - 5 = -3m\\[/tex]

When we solve for b, we get:

[tex]b = -3m + 5\\5 - 5 = m(3 - 3) (3 - 3)\\0 - 5 = m(3b - 3) (3b - 3)\\-5 = 3bm - 3m\\[/tex]

When we simplify, we get:

[tex]m = 5/(9b) (9b)\\[/tex]

Substituting this expression for m in the equation for the y-intercept b results in:

[tex]b = -15/(9b) + 5\\9b^2 = -15b + 45b\\9b^2 - 30b = 0\\3b(3b - 10) = 0\\b = 10/3\\(y - 5) = m(x - 3) (x - 3)\\(y - 5) = 5x/(9*10) - 1/3\\9y - 45 = 5x - 3\\5x - 9y = -42\\[/tex]

As a result, the equation of the straight line passing through (3,5) and having an x-intercept three times the y-intercept is:

5x - 9y = -42

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The correct option is (a), i.e. The mean would increase.

What is mean?

Mean is a measure of central tendency that is commonly used in statistics and mathematics. The mean of a set of numbers is calculated by adding up all the numbers in the set and dividing the sum by the total number of values in the set.

The mean of the number of air conditioner units sold by the 10 sales representatives last year can be calculated by adding up all the sales and then dividing by the total number of representatives, which is 10:

Mean = (6 + 8 + 10 + 11 + 12 + 16 + 17 + 21 + 32 + 36) / 10

= 169 / 10

= 16.9

So the mean number of air conditioner units sold per representative is 15.9.

If the representative who sold the lowest number of units left the department and his sales are cancelled out, the new sum of sales will be:

6 + 8 + 10 + 11 + 12 + 16 + 17 + 21 + 32 + 36 - 6 = 163

This is because we subtract the sales of the representative who left (which is 6 units in this case). The new mean can then be calculated by dividing this sum by the new total number of representatives, which is 9:

New mean = 163 / 9

= 18.11

So the new mean number of air conditioner units sold per representative is 18.11, which is higher than the original mean of 16.9. This is because removing the lowest value (which is smaller than the mean) increases the overall average.

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Answer:

The correct answer is:

x = 0°, 30°, 150°, 180°

This is because the sine function equals 0 at 0° and 180° and equals 1/2 at 30° and 150°.

Step-by-step explanation:

The frequency of a sound wave is the number of cycles it completes in a given amount of time. In this case, we can find the frequency of each sound wave by looking at the period of the functions.

The function y = 2sin2x has a period of π (since 2sin(2x) has a period of π/2, which is then compressed horizontally by a factor of 2). The function y = sinx has a period of 2π.

If the frequencies are the same, then the two functions must complete an equal number of cycles in the interval [0°, 360°), which is the same as the interval [0, 2π) in radians.

Let's first look at the function y = sin x. It completes one cycle in the interval [0, 2π), so we can say that it completes n cycles in the same interval, where n is an integer.

Now let's look at the function y = 2sin2x. It completes two cycles in the interval [0, π), so it completes four cycles in the interval [0, 2π). Therefore, we can say that it completes m cycles in the interval [0, 2π), where m is an integer.

For the frequencies to be the same, we need to find values of n and m such that:

n = m

Solving for n and m, we get:

n = m = 2

So both functions complete two cycles in the interval [0, 2π). We can find the times when this occurs by setting the angles in radians equal to multiples of 2π/2, or π:

2sin2x = sin x

2sin2x - sin x = 0

sin x (2sin x - 1) = 0

sin x = 0 or 2sin x - 1 = 0

sin x = 0 when x is an integer multiple of π.

2sin x - 1 = 0 when sin x = 1/2, which occurs when x = π/6 or x = 5π/6.

Therefore, the frequencies of the sound waves are the same at x = π/6, x = π/2, x = 5π/6, and x = 3π/2.

The correct answer is:

x = 0°, 30°, 150°, 180°

This is because the sine function equals 0 at 0° and 180° and equals 1/2 at 30° and 150°.

We have to calculate the number of combinations of 3 laser printers that can be selected from the 30 shipped. In this case, the number of possible combinations is 4060.

The combination can be calculated using the formula

ⁿCr = n! / r! (n-r)!

Where n is the total number of items and r is the number of items chosen. In this case, n is 30 and r is 3.

³⁰C₃= 30! / (3! * (30-3)!) ⇒ 30! / (6 * 24)

⇒ 30 * 29 * 28 / 6

⇒ 4,060

Therefore, the answer is 4060 possible combinations of 3 laser printers that can be selected from the 30 shipped.

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Answer:

2,188,180

Step-by-step explanation:

since 0 can't give anything to 8 the number would stay the same

A man that is 6 feet tall cast a shadow that is 15 feet if a child Cassa shadow that is 10 feet long then the child is 4 feet tall.

To find the height of the child, we can use the concept of similar triangles. The man's height and shadow form one

triangle, and the child's height and shadow form another.

Step 1: Identify the given information.

Man's height = 6 feet

Man's shadow = 15 feet

Child's shadow = 10 feet

Step 2: Set up a proportion using the given information.

Man's height/Man's shadow = Child's height/Child's shadow

6/15 = Child's height/10

Step 3: Solve for Child's height.

To do this, cross-multiply:

6 × 10 = 15 × Child's height

60 = 15 × Child's height

Step 4: Divide both sides by 15 to find the Child's height.

Child's height = 60 / 15

Child's height = 4 feet

So, the child is 4 feet tall.

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Answer:

$51

Step-by-step explanation:

You convery the percentage into a decimal, by dividing it by a hundred.

15÷100= 0.15

then you multiply the decimal and the price.

60×0.15= 9.

The question said it got cheaper so we have to subtract 9 from the original price.

60-9=51.

The linear equation is y = 6x + 5

A statement that shows the equality of two mathematical expressions is known as an equation. The goal is typically to ascertain the values of the variables that keep the equation true, and it may have one or more variables. In that both sides must be equal for an equation to hold true, it might be likened to a balance scale.

To find the equation for the pricing formula, we can use the slope-intercept form of a linear equation:

y = mx + b

where y is the cost, x is the number of gallons, m is the slope (i.e., the rate of change of the cost per gallon), and b is the y-intercept (i.e., the cost when x = 0).

Using the given information, we can calculate the slope:

m = (35 - 11) / (5 - 1) = 24 / 4 = 6

The y-intercept can be found by plugging in one of the points:

11 = 6(1) + b

b = 5

Therefore, the linear equation for the pricing formula for Logan's Paint is:

y = 6x + 5

where y is the cost in dollars and x is the number of gallons.

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Answer:

tesla electric company:

hours :cost

0:$50

1:$ 75

2: $100

3: $125

4: $150

Ac-Ad electric

hours: cost

0: $0

1: $50

2: $100

3: $150

4: $200

1/4 square centimeter is therefore equal to 1/2 square centimeter.

In math, what is a fraction?

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears inside the numerator and denominator of a complex fraction. The numerator of a proper fraction has a smaller denominator.

While "1/2-centimeter square" refers to a square having the side length of half a centimeter, the marking "1/2 square centimeter" typically refers to an area equal half a square centimeter. Even though these aren't the same object, we can still calculate the ratio of one to the other.

The area of such a square of side length 1/2 centimeter is:

(1/2 cm) x (1/2 cm) = 1/4 square centimeter

We may divide 1/4 by 1/2 to determine the percentage of 1/2 square centimeter that corresponds to 1/4 square centimeter:

(1/4 square cm) ÷ (1/2 square cm) = (1/4) x (2/1) = 1/2

Hence, 1/4 square centimeter is equal to 1/2 square centimeter in size.

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The dimensions of the box that will minimize the cost of manufacturing it: base = 9.04 in and y = 3.01 in

And the minimum cost is 32.65 cents

Let us assume that x represents the base side of the box, and y represents the height of the box.

The volume of the box would be:

V = x²y

246 = x²y        ........(1)

The cost of the material for the base is 0.2 cents per square inch, and the cost of the material for the sides is 0.3 cents per square inch.

Since this box has 4 sides and 1 base, the total cost would be,

C = (0.2 × x² × 1) + (0.3 × 4 × xy)

C = 0.2x² + 1.2x(246x⁻²)              (from (1) y = 246x⁻²)

C = 0.2x² + 295.2 x⁻¹

Consider derivative with respect to x,

dC/dx = 0.4x - 295.2 x⁻²

Consider dC/dx = 0

So,  0.4x - 295.2 x⁻² = 0

0.4x³ =  295.2

x³ = 738

So, x = 9.04

So, the value of y would be:

y = 246 x⁻²

y = 246 × (9.04)⁻²

y = 3.01

So, the minimum cost would be:

C = (0.2 × 0.04² × 1) + (0.3 × 4 × 9.04 × 3.01)

C = 32.65

Therefore, the minimum cost is: 32.65 cents

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The total amount Julio spent on a salad and a container of yogurt in the form of note and coin is equal to $6.38.

To determine how much Julio spent while buying  a salad and a container of yogurt, we have to multiply the value of each notes into their quantity then add all of them.

Number of 25 cents coins = 4

⇒ 4×0.25 = 1.00

Number of 5 dollar note = 1

⇒ 1×5 = 5.00

Number of 10 cents coins = 3

⇒ 3×0.10=0.30

Number of 1 cents = 3

⇒ 3×0.01=0.03

Number of 5 cents = 1

⇒ 1×0.05=0.05

Julio spent = 1.00 + 5.00 + 0.30 + 0.03 + 0.05

                  = $6.38

Therefore, the total amount Julio spent on a salad and a container of yogurt in the form of note and coin is equal to $6.38.

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The complete question is :

Julio buys a salad and a container of yogurt. These bills and coins shown in attached image represent the cost of each item. How much did Julio spend in all?

Concept: "Logos" has greatly affected Western philosophy and a variety of scientific disciplines. Acknowledgement: the interaction between logical reasoning and empirical observation as well as the influence of language and discourse worldview.

For the concept:

Topic: The significance of the Greek philosophical idea of "Logos" in contemporary scientific disciplines.

Greek philosophy's basic idea of "Logos" has had numerous interpretations throughout history. The word "logos" is most commonly used to refer to reasoned discourse and language. It is frequently linked to human conversation and reasoning as well as the cosmic or divine principle that creates and sustains the universe.

The significance of "Logos" can be observed in its impact on contemporary scientific disciplines, including, but not limited to, biology, psychology, and technology. For instance, the word "biology" is derived from the Greek terms "bios" (life) and "logos" (word or reason), illustrating the notion that the study of life necessitates both practical observation and logical analysis.

Parallel to this, the scientific discipline of psychology, which examines how the human mind and behaviour function, gets its name from the Greek words "psyche," which means "soul," and "logos," which means "reason." This illustrates the notion that both empirical research and theoretical analysis are necessary for the study of the mind and behaviour.

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Translation: The first schools of classical philosophy founded by the Greek word "logos" are widely understood as the apex of Western rationalist culture. In actuality, he is the one who gave the titles of numerous branches of science, including philology, psychology, technology, and biology. The idea of "logos" does not have such an abstract meaning because it involves both internal and exterior mental and physical actions, as well as the mental idea and word pronunciation. Topic: Main Idea:

Answer:

Like terms

Step-by-step explanation:

Are the terms that contain same variables, same exponents of variables and same coefficients.

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The number of rubber bands that Alana has to add to the ball to increase its diameter by 1 cm is 74.

Given that:

Alana is making a ball out of rubber bands.

The volume of the ball with 54 rubber bands is found as below:

Diameter of the ball = 3 cm

The radius of the ball is half of the diameter.

So, radius, r = 1.5 cm

So, the volume of the ball formed by 54 rubberbands is:

[tex]V=\frac{4}{3}\pi r^3[/tex]

Substitute r = 1.5.

[tex]V=\frac{4}{3} \pi (1.5)^3[/tex]

[tex]V=4.5\pi[/tex]

Now, the volume of the ball formed by 1 rubber band or the volume of the rubber band is:

[tex]V(r)=\frac{4.5\pi }{54}[/tex]

[tex]V(r)=\frac{\pi }{12}[/tex]

When the diameter increased by 1 cm, the new diameter is 4 cm and thus the radius is 2 cm.

So, the increase in volume is:

[tex]\frac{4}{3} \pi (2)^3-\frac{4}{3} \pi (\frac{3}{2} )^3=\frac{37\pi }{6}[/tex]

Now, divide this by the volume of one rubber band to get the number of rubber bands to be added.

[tex]\frac{\frac{37\pi }{6}}{\frac{\pi }{12} } =74[/tex]

Hence, the number of bands added is 74.

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We can be 98% cοnfident that the true difference in mean amοunt οf fοοd Buster eats when οffered Busted Nuggets and Busted Tenders is between -14.566 and -7.634 grams

Calculate the sample mean difference and the standard errοr οf the difference in οrder tο build the cοnfidence interval fοr the difference in the mean amοunt οf fοοd that Buster cοnsumes when served Busted Nuggets and Busted Tenders.

The sample mean difference is:

X1 - X2 = 152.6 - 163.7 = -11.1 grams.

The standard errοr οf the difference can be calculated as fοllοws:

SE = √(S1²/n1 + S2²/n2)

where S1 and S2 are the sample standard deviatiοns οf the twο grοups and n1 and n2 are the sample sizes.

Substituting the values, we get:

SE = √(4.45²/31 + 5.75²/31) = 1.463

ME = t x (SE) = 2.365 x 1.463 = 3.466

Finally, the cοnfidence interval fοr the difference in mean amοunt οf fοοd Buster eats is:

-11.1 - 3.466 < µ1 - µ2 < -11.1 + 3.466

-14.566 < µ1 - µ2 < -7.634

Hence, we have a 98% cοnfidence level that Buster actually cοnsumes between -14.566 and -7.634 grammes less fοοd οn average when given the chοice between Busted Nuggets and Busted Tenders. This periοd can be understοοd as Buster favοring Busted Tenders because οf the negative.

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Answer:

how web is it you feel like a a a a a a a a a make

Step-by-step explanation:

hf and I have been working on the topic on the topic on the topic on the topic on the topic ona the topic on the topic on the topic on the topic on the

The probability that both customers say that the service is poor is 0.0588 or 5.88%.

To determine the probability that both customers say the service is poor, use the binomial distribution and the following formula:P(X = k) = (nCk) * p^k * (1 - p)^(n - k)Where:P(X = k) represents the probability that k successes occurn is the sample sizep is the probability of successk is the number of successes requested(1 - p) represents the probability of failure.Substitute the given values and calculate:P(X = 2) = (2C2) * (140/500)^2 * (1 - 140/500)^(2 - 2) = 0.0588 or 5.88%

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Answer:

45

Step-by-step explanation:

[tex]g(f(x))=5(x+6)[/tex]

[tex]g(f(3))=5(3+6)\\[/tex]

[tex]g(f(3))=5(9)\\[/tex]

[tex]g(f(3))=45[/tex]

Answer:

f(x) =x + 6g(x) =5x =

Calculate the formula weights:

mass of mole of

F(x) = x + 6g (x) = 5x = 19g

Answer:

length times with equals to base times height

Step-by-step explanation:

length times with times height equals to 3400

using what we know about whole number division can be helpful when dividing with fractions. We can use the inverse operation of multiplication, simplify fractions, and use estimation to check our work and ensure that our division is accurate.

When dividing with fractions, one can use what they know about whole number division to check their work. This is because the rules of division remain the same for both whole numbers and fractions. One important rule is that division is the inverse operation of multiplication. In other words, when we divide, we are essentially finding how many times one number (the divisor) fits into another number (the dividend).

To check our work when dividing with fractions, we can use the same approach. We can multiply the quotient (the result of our division) by the divisor to see if we get back the dividend. If we do, then we know that our division was correct. For example, if we divide 3/4 by 1/2 and get a quotient of 3/2, we can check our work by multiplying 3/2 by 1/2.

Another important rule is that we can simplify fractions before dividing them to make the process easier. This means that we can divide both the numerator and the denominator by a common factor to get an equivalent fraction with smaller numbers. For example, if we want to divide 6/8 by 2/3, we can simplify 6/8 to 3/4 and 2/3 to 8/12. Then we can divide 3/4 by 8/12, which is much easier.

Finally, we can also use estimation to check our work when dividing with fractions. Estimation involves rounding the fractions to the nearest whole number or using benchmarks, such as 1/2 or 1, to get an approximate answer. This can help us quickly check if our quotient is reasonable or if we made an error in our division.

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Answer:

Step-by-step explanation:

To find:-

Answer:-

We are here given that, out of the total money made 20% was spent on food .

To calculate the money spent on food we need to find out 20% of $25,00 .

So that,

==> 20% of $25,000

==> 20/100 * $25,000

==> 0.2 * $25,000

==> $5,000

Hence the total money spent on food was $5,000 .

The undefined terms in this axiom set are "line" and "point." These terms are not defined within the axioms themselves and are assumed to be understood.

The axiomatic system is consistent. The axioms do not contradict each other, and it is possible to construct a model of the system that satisfies all the axioms.

For example, we can imagine a Euclidean plane where each line is a set of three non-collinear points, and each point is contained by exactly two lines. Two distinct lines in this plane intersect at exactly one point, satisfying all the axioms.

The specific property of this axiomatic system is that it defines a Euclidean plane, which is a specific type of geometry characterized by the three axioms given.

The axioms capture some of the fundamental properties of Euclidean geometry, such as the existence of points and lines, the intersection of lines, and the relationship between points and lines.

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