what is true about an equation with infinite solutions

Answer:

  C.  51 -10√2

Step-by-step explanation:

You want the square of 5√2 -1.

The square of 5√2 -1 can be found using the distributive property.

  [tex](5\sqrt{2}-1)^2=(5\sqrt{2}-1)(5\sqrt{2}-1)\\\\=5\sqrt{2}(5\sqrt{2}-1) -1(5\sqrt{2}-1)\\\\=(5\sqrt{2})(5\sqrt{2}) -5\sqrt{2}-5\sqrt{2}+1\\\\=25(\sqrt{2})^2-10\sqrt{2}+1\\\\=25\cdot2+1-10\sqrt{2}=\boxed{51-10\sqrt{2}}[/tex]

The equivalent expressions are:

a) 4*(x + 2) = 4x + 8

b) 4*(2x + 3) = 8x + 12

c) (6 + 8)*x = 14*x

d) 6*(x + y + z) = 6x + 6y + 6z

This is a property of the multiplication, and it says that we can distribute products in the following way:

A*(B + C) = A*B + A*C

So let's do that.

a) 4*(x + 2) = 4*x + 4*2 = 4x + 8

b) 4*(2x + 3) = 4*(2x) + 4*3

                    = 8x + 12

c) (6 + 8)*x = 6*x + 8*x = 14*x

d) 6*(x + y + z) = 6x + 6y + 6z

These are the equivalent expressions.

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The expression is equivalent to 9250.

Scientific notation is a way of writing very large or very small numbers in the powers of 10.

Given is the expression -

92.5 x 10²

We can write the expression as -

92.5 x 10²

925/10 x 100

925 x 10

9250

Therefore, the expression is equivalent to 9250.

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{

Question in english -

what is 92.5 × 10 times the power of 2​

}

Answer:

Hi

Kyle's velocity vectors have opposite directions.

Step-by-step explanation:

When Kyle is walking away from his house, his velocity vector is pointing in the positive direction, representing the movement of his position in a specific direction. But after ten minutes, when he turns around and walks home, his velocity vector changes direction to point in the opposite direction, now representing his movement towards his house. The difference between the two velocity vectors is that they are in opposite directions.

Without the actual values of b0 and b1, it is not possible to determine the predicted explanatory value. The correlation coefficient alone does not give enough information to make this prediction.

To find the predicted explanatory value that gives an average response value of 150, you would need to use the regression equation.

The regression equation takes the form:

y = b0 + b1x

where y is the response variable, x is the explanatory variable, b0 is the y-intercept, and b1 is the slope.

To find the x value that gives you a y value of 150, you would rearrange the equation as follows:

x = (y - b0)/b1

Plug in 150 for y and the y-intercept and slope values from your regression analysis to find the predicted explanatory value.

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The domain and range of the relation is

Domain = {1, 2, 3, 4, 5}

Range = {3, 5, 7, 9}

Option D is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

{(1, 3), (2, 5), (3, 7), (4, 9), (5,9)}

It is in ordered paired as (x, y).

x-coordinate is the domain and the y-coordinate is the range.

So,

Domain = {1, 2, 3, 4, 5}

Range = {3, 5, 7, 9}

Thus,

Domain = {1, 2, 3, 4, 5}

Range = {3, 5, 7, 9}

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Answer:

Step-by-step explanation:

35% of 255 = 89.25

255-89.25 =165.75

Answer:11x

Step-by-step explanation:

(−6x−2)+(6x2−5x−10)

first solve whats inside the brackets.

=-6x-2+(12-5x-10)

=-6x-2+(2-5x)

then open the brackets and solve the rest using order of operations.

=-6x-2+2-5x

=11x

Answer:The linear function f with the given points is: f(x) = 3.

The linear function is a straight line that passes through two points (0, 3) and (-6, 3). This means that the equation of the line is given by y = mx + c, where m is the gradient of the line and c is the y-intercept. In this case, the 0,3 and -6,3 points have the same y-value, so the y-intercept is equal to 3.

To find the gradient of the line, we must use the formula m = (y2-y1)/(x2-x1). Therefore, the gradient of the line is m = (3-3)/(-6-0) = 0, meaning that the equation of the line is y = 3.

Step-by-step explanation:

The linear function f with the given points is: f(x) = 3.

The linear function is a straight line that passes through two points (0, 3) and (-6, 3). This means that the equation of the line is given by y = mx + c, where m is the gradient of the line and c is the y-intercept. In this case, the 0,3 and -6,3 points have the same y-value, so the y-intercept is equal to 3.

To find the gradient of the line, we must use the formula m = (y2-y1)/(x2-x1). Therefore, the gradient of the line is m = (3-3)/(-6-0) = 0, meaning that the equation of the line is y = 3.

The required volume of the earth in cubic kilometers as per given hectares of land and its depth is equal to 0.0261 km³.

Hectare of land consumed by an open -pit coal mine = 87 hectares

Convert hectare into square meters

1 hectares = 10⁴ square meter

87 hectares = 87 × 10⁴ square meter

Depth = 30 m

Area of land = 87 × 10⁴ square meter

Volume of earth = area of land × depth

⇒ Volume of earth = 87 × 10⁴ m² × 30 m

⇒ Volume of earth = 261 × 10⁵ m³

1 kilometer = 10³meters

⇒1m³ = 10⁻⁹ km³

Volume of the earth = 261 × 10⁵ × 10⁻⁹ km³

⇒Volume of the earth = 261 × 10⁻⁴ km³

                                     = 0.0261 km³

Therefore, the volume of the earth as per given area of land and depth is equal to 0.0261 km³.

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As a result, the area of the surface formed by rotating the given curve about the x-axis throughout the period [9, 20] is 864π.

The size of a region on a surface is measured in area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina.

Here,

The area of the surface generated when a curve is revolved about an axis is known as the surface area of revolution and can be calculated using the formula:

A = 2π ∫ y dx

where y is the equation of the curve being revolved and the integral is taken over the interval [a,b] in which the curve is being revolved.

In this case, the curve is given by y = 8√x on the interval [9, 20]. So, the surface area of revolution is:

A = 2π ∫_9^20 8√x dx

This integral can be evaluated using substitution. Let u = √x, so that du = dx / 2√x and x = u^2. Then:

A = 2π ∫_3^4 8u * 2u du

= 2π * 8 * ∫_3^4 u^2 du

= 2π * 8 * [u^3/3]_3^4

= 2π * 8 * (64/3 - 27/3)

= 2π * 8 * (37/3)

= 864π

So, the area of the surface generated when the given curve is revolved about the x-axis over the interval [9, 20] is 864π.

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Answer:

24

Step-by-step explanation:

It would take 33,792,000 dollar bills laid end to end to enclose a square mile.

To calculate this, we use the formula for the perimeter of a square: P = 4s, where P is the perimeter and s is the length of one side. Since the length of one side of a square mile is 5,280 feet, we can calculate the perimeter of a square mile in feet: P = 4(5280 ft) = 21,120 ft. Since one dollar bill is 6.14 inches long, we can convert this to feet by dividing by 12 (1 ft = 12 inches): 21,120 ft / 12 inches/ft = 1,760 ft. Finally, we can calculate the number of dollar bills needed by dividing the perimeter in feet by the length of the dollar bill in feet: 1,760 ft / 0.514 ft = 33,792,000 dollar bills.

It would take 33,792,000 dollar bills laid end to end to enclose a square mile.

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This function satisfies the conditions given: it is an nth-degree polynomial with real coefficients, it has zeros at -1, 4, and 4 + 4i, and it has the value of -150 at x = 1.

A polynomial is a mathematical expression that is composed of variables and coefficients, which are combined using only addition, subtraction, and multiplication. The variables in a polynomial can be raised to whole number powers, and the highest degree of a polynomial (i.e., the highest power to which a variable is raised) is known as the degree of the polynomial. For example, the polynomial 3x^2 + 2x + 1 has a degree of 2. The terms in a polynomial are usually arranged in descending order of degree, so that the first term has the highest degree and the last term has a degree of zero. The sum or difference of two or more polynomials is also a polynomial.

To find an nth-degree polynomial function with real coefficients that satisfies the given conditions, we can use the following process:

1. Write the polynomial in factored form using the zeros:

p(x) = a(x-1)(x-4)(x-(4+4i))(x-(4-4i))

2. Use the value of f(1) to find the leading coefficient a:

f(1) = p(1) = a(0)(0)(0)(0) = -150

a = -150

3. Write the polynomial in expanded form:

p(x) = -150(x-1)(x-4)(x-(4+4i))(x-(4-4i))

The resulting polynomial function is:

p(x) = -150(x-1)(x-4)(x-(4+4i))(x-(4-4i))

This function satisfies the conditions given: it is an nth-degree polynomial with real coefficients, it has zeros at -1, 4, and 4 + 4i, and it has the value of -150 at x = 1.

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The rate is 150 square meters per hour. Then the area of the oil spill after 2 hours will be 300 square meters.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

An oil spill spreads 25 square meters every 1/6 hour. Then the number of square meters in each hour is given as,

Rate = 25 / (1/6)

Rate = 25 x 6

Rate = 150 square meters per hour

The area of the oil spill after 2 hours will be given as,

⇒ 150 x 2

⇒ 300 square meters

Thus, the area of the oil spill after 2 hours will be 300 square meters.

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Therefore , the solution of the given problem of fraction comes out to be $25 she get paid per hour.

A whole can be represented by any class of similar sums or fractions. A fraction is used to express the amount of a particular size in standard English. 8, 3/4. Fractions are also wholes. In mathematics, numbers are represented by the fraction to numerator ratio. All of these fractions are simple integers. The fraction of a challenging fraction contains a fraction. due to the variations in actual fraction calculations, numerators, and numerators.

Here,

Given :

=> new job 2 weeks

=> amount = $875

35 hours work per week

So,

Per hour she get paid is :

=> 875/35

=> 25

Thus,

$25 she get paid.

Therefore , the solution of the given problem of fraction comes out to be $25 she get paid per hour.

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There are 64 ways to choose a single class representative.

To find the total number of ways to choose a single class representative, we add the number of students in each college: 18 students from the College of Liberal Arts and Social Sciences, 19 students from the College of Education, and 27 students from the College of Science and Health.

This gives us a total of 18 + 19 + 27 = 64 students. To choose a single class representative, we can choose any one of these 64 students, so there are 64 ways to choose a single class representative.

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The answer can be solved by using the kinematic equation, S= ut+at²/2. Here the time taken by the feather to fall from 75 feet will be 2.16 s.

Here a feather is dropped from a height of 75 ft. All other units are in SI system. So we have to convert the height to meters.

75 ft = 75/ 3.281 = 22.86 m.

We are neglecting the frictional force, or any other force acting on the feather. If the feather is under free fall, we can use the kinematic equation,

   S = ut + at²/2

S is the displacement, here the height = 22.86 m

u is the initial velocity, which is 0

t is the time

a is acceleration, here a= g, acceleration due to gravity = 9.8 m/s².

S = 0×t + 9.8t²/2

22.86 = 4.9t²

t² = 22.86/4.9

   = 4.665

t = √4.665 = 2.159 s = 2.16 s

So the time taken for the feather to reach water will be 2.16 s.

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Answer:

x=4

Step-by-step explanation:

pls tell me if wrong have a good day/night<3

Probability: P(education beyond high school but not a bachelor's degree) = (number of young adults with education beyond high school but not a bachelor's degree) / (total number of young adults).

The probability that a randomly chosen young adult has some education beyond high school but not a bachelor's degree would be:

P(education beyond high school but not a bachelor's degree) = (number of young adults with education beyond high school but not a bachelor's degree) / (total number of young adults)

where "number of young adults with education beyond high school but not a bachelor's degree" refers to the count of individuals in the population who meet this criteria, and "total number of young adults" refers to the count of all individuals in the population who are considered young adults.

The formula calculates the probability of a certain event by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, the event is a randomly chosen young adult having some education beyond high school but not a bachelor's degree. The numerator, "number of young adults with education beyond high school but not a bachelor's degree," represents the favorable outcomes, while the denominator, "total number of young adults," represents all possible outcomes.

By dividing the favorable outcomes by the total number of possible outcomes, we get the probability of the event occurring, which is a value between 0 and 1. The closer the value is to 1, the higher the probability that the event will occur. The closer the value is to 0, the lower the probability that the event will occur. This formula allows us to quantify the likelihood of an event occurring in a population based on the available data.

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Assuming a binomial distribution for the number of auto accidents. If 7 in 10 auto accidents involve a single vehicle, the probability, p =[tex]\frac{7}{10}[/tex] = 0.7

Then the probability that the accident involved multiple vehicles is

q = 1 - p = 1 - 7/10 = 3/10 = 0.3

Since 14 accidents are randomly selected, n = 14

The formula for binomial distribution is expressed as

P(x = r) = nCr × q*(n - r) × p*r

a) we want to determine P(x = 4) =

P(x = 4) = 14C4 × [tex]0.3^{10}[/tex] × 0.7^4

P(x = 4) = 0.00142

b) we want to find P(x lesser than or equal to 4) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P( x = 4)

P(x = 0) = 14C0 × [tex]0.3^{14}[/tex] × 0.7^0 = 0.00000004783

P(x = 1) = 14C1 × [tex]0.3^{13}[/tex] × 0.7^1 = 0.00011

P(x = 2) = 14C2 × [tex]0.3^{12}[/tex] × 0.7^2 = 0.00002

P(x = 3) = 14C3 ×[tex]0.3^{11}[/tex]  × 0.7^3 = 0.00022

P(x = 4) = 0.00142

P(x lesser than or equal to 4) = 0.00000004783 + 0.00011 + 0.00002 + 0.00022 + 0.00142 = 0.00177

c) p = 0.7, q = 0.3

P(x = 5)= 14C5 × 0.7^(14 - 5) × 0.3^5 = 0.19631

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The cost of the car leasing for 1 month is $31.25.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Cost of the car leasing for 24 months = $750

Cost of the car leasing for 1 month.

= 750 ÷ 24

= $31.25

Thus,

The monthly cost of car leasing is $31.25.

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The complete question:

Keely is looking at leasing a car for 24 months in order to lease the car she needs to give the dealership $750.

Find the monthly charge for leasing the car.

[tex](343a)^{3}[/tex] - [tex](1000b)^{3}[/tex] can be factorised as (343a - 1000b)(343[tex]a^{2}[/tex] + 1000ab + 1000[tex]b^{2}[/tex]).

Expression is a mathematical combination of symbol such as number and operators which produce the mathematical result and expression.

(343a - 1000b)(343[tex]a^{2}[/tex] + 1000ab + 1000[tex]b^{2}[/tex])

This expression can be factorised as the product of two binomials. The first binomial is (343a - 1000b). This can be seen by subtracting 1000[tex]b^{3}[/tex] from 343[tex]a^{3}[/tex], leaving us with 343[tex]a^{3}[/tex] - 1000[tex]b^{3}[/tex], which can be written as (343a - 1000b).

The second binomial is (343[tex]a^{2}[/tex] + 1000ab + 1000[tex]b^{2}[/tex]). This can be seen by expanding the cube of (343a - 1000b), leaving us with (343[tex]a^{2}[/tex] - 1000[tex]b^{2}[/tex] + 2000ab). Rearranging this expression gives us (343[tex]a^{2}[/tex] + 1000ab + 1000[tex]b^{2}[/tex])

Therefore, 343[tex]a^{3}[/tex] - 1000[tex]b^{3}[/tex] can be factorised as (343a - 1000b)(343[tex]a^{2}[/tex] + 1000ab + 1000[tex]b^{2}[/tex]).

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If a cube is rolled 24 times and lands on 2 four times and on 6 three times , then the experimental probability of not landing on a "6" is 0.171   .

on a cube there are total 6 outcomes ,

the probability of getting "2" on a single cube is = P(2) = 1/6  ;

the probability of getting "6" on a single cube is = P(6) = 1/6  ;

the probability of the cube not landing on 6 is = P'(6) = 5/6  ;

Since the cube is rolled 24 times , the experimental probability of not landing on "6" is

⇒ P(not 6) = ²⁴C₅×(1/6)⁵×(5/6)¹⁹ ;

On simplifying ,

we get ;

⇒ P(not 6) = 0.171  .

Therefore , the experimental probability of not landing on a 6 is 0.171  .

The given question is incomplete , the complete question is

A number cube is rolled 24 times and lands on 2 four times and on 6 three time. Find the experimental probability of not landing on a 6 .

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The pattern associated with the scatter plot is given as follows:

There is a positive nonlinear association.

The scatter plot shows a series of points in (input, output) format, in which the input is the time studying in minutes and the output is the grade.

As the increasing graph shows, the more a person studies, the better the grade, hence there is a positive relationship among the variables.

The increase is slow initially while it has a higher rate for a higher number of minutes, hence the association is also nonlinear.

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you should mix 4.5 quarts of 100% juice and 1.5 quarts of 20% juice. a=4.5, b= 1.5

The US liquid quart is equivalent to two liquid pints, or one-fourth US gallon (57.75 cubic inches, or 946.35 cubic centimetres), and the US dry quart is equivalent to two dry pints, or 1/32 bushels (67.2 cubic inches, or 1,101.22 cubic cm). 32 ounces, 2 pints, 4 cups, and 14 gallon are all equivalent to one US liquid quart. When converting any dry component, keep in mind that a dry quart is equivalent to 4.6546 cups. A quarter gallon is equal to one quart in English (symbol: qt). The liquid and dry quarts of the US customary system and the imperial quart of the British imperial system are the three types of quarts now in use. They all generally measure one litre.

Let you should mix a quarts of 100% juice and b quarts of 20% juice.

[tex]a+b=6[/tex]

100%a+20%b=6*8%

By solving the system of equation.

a=4.5

b= 1.5

So you should mix 4.5 quarts of 100% juice and 1.5 quarts of 20%.

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The solution is, the circumference of the circle with radius 14in. is  87.96 inch.

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.

Perimeter refers to the total outside length of an object,

here, we have,

the radius = r = 14 inch.

we know,

circumference = 2*pi* r

so, calculating we get,

circumference = 87.96 inch.

Hence, The solution is, the circumference of the circle with radius 14in. is  87.96 inch.

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The slopes are :- -5, 1/3, -1/5, undefined, 1/4, -2/3, -1, -1, -2/3 and -5/2

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

Given are the equations of the lines, we need to find the slope of the equation,

The general equation of a line is given by,

y = mx + c, where m is the slope and c is the y-intercept of the line.

So, finding slope of given equations by comparing them with the general equation,

1) y = -5x-1

m = -5, slope = -5

2) y = x/3-4

m = 1/3, slope = 1/3

3) y = -x/5-4

m = -1/5, slope = -1/5

4) x = 1,

Since, x=1 is a vertical line, the slope is undefined.

5) y = x/4+1

m = 1/4, slope = 1/4

6) y = -2x/3-1

m = -2/3, slope = -2/3

7) y = -x+2

m = -1, slope = -1

8) y = -x-1

m = -1, slope = -1

9) 2x+3y = 9

Converting into slope-intercept form,

2x+3y = 9

3y = -2x+9

y = -2x/3+3

m = -2/3, slope = -2/3

10) 5x+2y = 6

Converting into slope-intercept form,

5x+2y = 6

2y = -5x+6

y = -5x/2+3

m = -5/2, slope = -5/2

Hence, the slopes are :- -5, 1/3, -1/5, undefined, 1/4, -2/3, -1, -1, -2/3 and -5/2

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