What is the square of (- 1?

The number of gallons of gasoline pumped by a filling station during a day represents a B: "quantitative " type of variable.

Quantitative variables are data about numeric values such as how much; how often; or how many.  In other words, quantitative variables are referred to as any variables that represent amounts, such as age, height, or weight.

In the given case, it is talked about the number of gallons of gasoline filled during a day; since it represents the quantity or number of gallons so it is a type of quantitative variable, representing the number of gallons of gasoline to be pumped.

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Steps which are required to solve quadratic equation by factoring are as follow :

1. Convert the equation into standard form.

2. calculate the factors of the equation by splitting or formula method.

3. Equate the factors to zero and get the value.

Example : Factors of x² + 4x + 4 = 0 are x = -2.

As given in the question,

Steps required to solve quadratic equation by factoring are given by :

Standard quadratic equation is : ax + by + c = 0

Two methods to solve quadratic equations are:

a. Splitting method

b. Formula  : x = ( - b ± √b² -4ac ) / 2a.

Consider a example:

x² + 4x = -4

1. Convert into standard from

x² + 4x + 4 = 0

solve it by splitting method :

x² + 2x + 2x + 4 = 0

⇒ x(x + 2 ) + 2 ( x + 2 ) =0

⇒ ( x + 2 ) ( x+ 2 ) = 0

⇒ x + 2 = 0

⇒ x = -2

Therefore, the steps required to solve quadratic equation are :

1. Convert the equation into standard form.

2. calculate the factors of the equation by splitting or formula method.

3. Equate the factors to zero and get the value.

Example : Factors of x² + 4x + 4 = 0 are x = -2.

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Answer:

3

Step-by-step explanation:

x = the third side

x² + ([tex]\sqrt{55}[/tex])²= 8²

x² = 64 - 55 = 9

x = [tex]\sqrt{9}[/tex] = 3

Answer:

roots are real and rational

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 ( a ≠ 0 ) , then the discriminant is

b² - 4ac

the discriminant informs on the nature of the roots

• if b² - 4ac > 0 then roots are real and irrational

• if b² - 4ac > 0 and a perfect square, then roots are real and rational

• if b² - 4ac = 0 , then roots are real and equal

• if b² - 4ac < 0 , then the roots are not real

for 2x² + 7x + 6 = 0 , in standard form

with a= 2, b = 7 , c = 6 , then

b² - 4ac = 7² - (4 × 2 × 6) = 49 - 48 = 1

since b² - 4ac > 0 and a perfect square, then the roots are real and rational

The absolute value of the number plotted on the number line is 1.25

Kinetic energy acquired by the body in 10 sec is 4000 J.

What is kinetic energy?

The energy that an object has as a result of motion is known as kinetic energy. It is described as the effort required to move a mass-determined body from rest to the indicated velocity. The body holds onto the kinetic energy it acquired during its acceleration until its speed changes.

Here. we ave

Given: A body of mass 5 kg initially at rest is subjected to a force of 20 N

Force = mass × acceleration

A= F/m

a= 4 m/s ².

We know that,

K.e = 1/2 mv²

To find v:-

V= u+at

V= 0+40

V= 40 m/s.

K.E = 1/2 ×5×40×40

K.E = 4000 J.

Hence, kinetic energy acquired by the body in 10 sec is 4000 J.

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At Nation Office Supply, Marley purchased 9 dozen notepads.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

At Nation Office Supply, pens are $1.69 per dozen and notepads are $4.59 per dozen.

Here, Marley purchases 9 dozen pens, and spend total $56.52.

Let number of notepads can she purchase = x

So, We can formulate;

⇒ 9 × $1.69 + $4.59x = $56.52

⇒ 15.21 + 4.59x = 56.52

⇒ 4.59x = 56.52 - 15.21

⇒ 4.59x = 41.31

⇒ x = 41.31 / 4.59

⇒ x = 9

Thus, Marley purchased 9 dozen notepads.

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The value of y after solving the given equation is -8.

We can calculate the value of y through the following method,

We have been provided with an exponential equation [tex]8^{y} = 16^{y+2}[/tex]

As we know, an exponential equation is an equation whose exponent or part of the exponent is a variable.

For solving an exponential equation, we need to use logarithms and their properties.

We can write [tex]8^{y}[/tex] also as [tex]2^{3y}[/tex] since we know that 2³ = 8

Similarly, we can write [tex]16^{y+2}[/tex] also as [tex]2^{4(y+2)}[/tex] since we know that [tex]2^{4}[/tex] = 16

Therefore we get the new equation as,

[tex]2^{3y}[/tex] = [tex]2^{4(y+2)}[/tex]

Now we will add log with base 10 on both the sides

Therefore the equation will become,

log₁₀ [tex]2^{3y}[/tex] = log₁₀ [tex]2^{4(y+2)}[/tex]

Since, according to the property of logarithm,

log₁₀ aᵇ = b log₁₀ a

Therefore,

3y log₁₀ 2 = 4(y + 2) log₁₀ 2

We can cancel out log₁₀ 2 on both sides

We get the equation as,

3y = 4(y + 2)

3y = 4y + 8

y = -8

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The value of x is 2 and NM = OL = 7

Now, According to the question:

What is a parallelogram?

A parallelogram is a special type of quadrilateral that has both pairs of opposite sides parallel and equal.

Given that, LMNO is a parallelogram and NM = x + 5 and OL = 2x + 3,

Since, we know that, opposite sides of a parallelogram are equal,

Therefore,

NM = OL

x+5 = 2x+3

x = 2

Therefore, NM = OL = 7

Hence, the value of x is 2 and NM = OL = 7

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The 30, 60, and 90 are special right triangles. the perimeter of the triangle is = [tex]a+b+c[/tex] =[tex]x+2x+x\sqrt{3}[/tex]

30,60,90 special right triangles because there is a relation between height, base, and the hypotenuse.

Point to be noted

the opposite side of [tex]30^o[/tex] is height, the opposite side of [tex]60^o[/tex] is base, and the opposite side of [tex]90^o[/tex] is the hypotenuse.

Assume the height of the triangle = [tex]x[/tex]

In this type of triangle, the hypotenuse is double of height,

so, hypotenuse = [tex]2x[/tex]

and the base of the triangle is [tex]\sqrt{3}[/tex] of the height.

Therefore, base = [tex]x\sqrt{3}[/tex]

so that, The perimeter of the triangle = [tex]x+2x+x\sqrt{3}[/tex]

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Formula used to calculate the y-intercept when coordinates of two points are given is as follow: y = mx + c where 'm' represents the slope and 'c' represents the y-intercept.

As given in the question,

Let us consider points of two coordinates be equal to

( x₁ , y₁ ) =  ( 2, 3 )

( x₂ , y₂ ) = ( 4, 7 )

Equation of the line is equal to :

( y - y₁ ) / ( x - x₁ )  = ( y₂ - y₁ ) / ( x₂ - x₁ )

⇒ ( y - 3 ) / ( x - 2 ) = ( 7 - 3 ) / ( 4 - 2 )

⇒ ( y - 3 ) / ( x - 2 ) = 2

⇒ y - 3 = 2x - 4

⇒ y = 2x - 1

Same as y = mx + c

Here c = -1

Here y-intercept is equal to -1 by substituting x = 0 we can get                 y - intercept.

Therefore, the value of y-intercept can be calculated with the coordinates of the given points using formula given by :

y = mx + c where 'c' represent y-intercept.

The given question is incomplete, I answer the question in general according to my knowledge:

If you're given coordinates of 2 points, how do you find the y-intercept?

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Karen adds up 4 consecutive odd integers ,the sum if the smallest one is 2m-1 is 8m + 8.

Since they are odd numbers, each time it must be +2 (since +1 goes odd, even, odd, even, etc.), therefore the result will be:

(2m - 1) + (2m + 1) + (2m + 3) + (2m +5) = 8m + 8

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The equation of equilibrium states that the sum of the forces in the x-direction must be zero.

Equation of equilibrium:

F_x = 0 = mgsinθ - mgsinϕ

mgsinθ = mgsinϕ

sinθ = sinϕ

θ = ϕ

The equation of equilibrium states that the sum of the forces in the x-direction must be zero. This means that the force due to gravity in the x-direction, mgsinθ, must be equal to the force due to gravity in the x-direction, mgsinϕ. This can be rearranged to sinθ = sinϕ, which means that the angles θ and ϕ must be equal. Thus, the relationship between angles θ and ϕ is that they are equal.

The equation of equilibrium states that the sum of the forces in the x-direction must be zero.

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Yes, George can be claimed as a dependent by his parents.

A dependent is a person who qualifies for a dependency exemption but is not the taxpayer or the taxpayer's spouse. Every exemption for a dependent reduces the amount of taxable income by the exemption amount.

If a full-time student, your child must be younger than 24 or younger than 19 years old. If your child is totally and permanently incapacitated, there is no upper age restriction. Are these your roommates? There are a few situations where your child does not need to live with you for more than half the year.

Your child must be younger than you and either be a "student" younger than 24 years of age as of the end of the calendar year, or be younger than 19 years old.

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The equation of a line that passes through the point (0,3) and has a gradient of 2 is: y = 2x + 3

We know that the point-slope form of equation of line is:

(y - y₁) = m(x - x₁)

where m is the slope (also called as gradient)

Here, we have been given a point (0, 3) and the slope of the line is 2.

Let us assume that (x₁, y₁) = (0, 3)

and slope (m) = 2

Using point-slope form of equation of line,

(y - y₁) = m(x - x₁)

(y - 3) = 2(x - 0)

y - 3 = 2x

y - 3 + 3 = 2x + 3

y = 2x + 3

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Answer:

  (c)  15 units

Step-by-step explanation:

Given a right triangle with hypotenuse 17 and one leg 8, you want the measure of the other leg.

The Pythagorean theorem tells you the relationship between the sides of a right triangle:

  a² +b² = c² . . . . . . where c is the hypotenuse

  a² +8² = 17² . . . . . . using given values of b, c

  a² = 289 -64 = 225 . . . . subtract 8²

  a = √225 = 15

The length of segment BC is 15 units.

__

Additional comment

These side lengths {8, 15, 17} can be considered to be a "Pythagorean triple." It is one of a few that often appear in algebra and geometry problems. Others include {3, 4, 5}, {5, 12, 13}, {7, 24, 25}. Multiples of these are also commonly seen, such as 2×{3, 4, 5} = {6, 8, 10}.

A inverse example is when two variables are inversely related, meaning that as one increases, the other decreases. For example, as the temperature outside rises, the amount of ice cream sold decreases.

Inverse relationship means that the two variables are directly proportional to each other; if one increases, the other decreases. An example of an inverse relationship is the relationship between the temperature outside and the amount of ice cream sold. As the temperature outside rises, the amount of ice cream sold decreases. This is because people are less likely to buy ice cream when it is hot outside.

A inverse example is when two variables are inversely related, meaning that as one increases, the other decreases. For example, as the temperature outside rises, the amount of ice cream sold decreases.

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By the definition of the mode, we can say the mode of this data is 33.

What is the mode?

The mode in statistics refers to a number in a set of numbers that appears the most often. For example, if a set of numbers contained the following digits, 1, 1, 3, 5, 6, 6, 7, 7, 7, 8, the mode would be 7, as it appears the most out of all the numbers in the set.

We have given,

Data set 18 16 11 45 33 16 33 14 18 33.

To find what is the mode for this data set.

Solution: We have given

Data set 18 16 11 45 33 16 33 14 18 33.

Mode: The mode of a set of data values is the value that appears most often.

So,

We can see the most repeated number is 33. ( 3 times)

Hence, by the definition of the mode, we can say the mode of this data is 33.

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No matter how far they reach, parallel lines are those that do not have a shared meeting point in the same plane.

If two lines cannot collide when extended in both directions to infinity, they are said to be parallel in a plane. Throughout the entire length, there remains a constant gap between two lines.

|| is the symbol used to represent the parallel lines. Assuming that lines "a" and "b" are parallel to one another, we may indicate this using the symbol "a||b," which means "a is parallel to b."

We need a ruler and a compass to create a line parallel to the other line starting from an outside point. The diagram of parallel line is given below:

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The given options (i), (ii) and (iv) are all solutions of the equation. Option (iii) is not a solution of the equation since x=-1/2 does not equal 3 or -2.

The given equation is 2x2 - 5x - 3 = 0. The solutions of a quadratic equation are found by setting the equation equal to zero and solving for x. The solutions of this equation can be found by using the Quadratic Formula:

x = [-b ± (√b2 – 4ac)] / 2a

Using this formula:

x = [-(-5) ± (√(-5)2 – 4(2)(-3))] / 2(2)

x = [5 ± (√25 + 24)] / 4

x = [5 ± (√49)] / 4

x = [5 ± 7] / 4

Therefore, the solutions are x = 3 and x = -2.

The given options (i), (ii) and (iv) are all solutions of the equation. Option (iii) is not a solution of the equation since x=-1/2 does not equal 3 or -2.

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Use the section formula to get the coordinates of a point that separates a line segment outside or internally in a specific ratio.

By building two right triangles and applying AA similarity, the section formula can be obtained. After determining the ratio of the triangle's side lengths in terms of the supplied ratios, we may solve for x and y to determine the coordinates of the point that divides the line segment.

To determine the coordinates of a point that splits a line segment externally or internally in a certain ratio, apply the section formula. A line segment's midpoint can be determined using this technique as well.

By section formula, we have, if (x, y) divides the line segments joining [tex]$\left(x_1, y_1\right)$[/tex] and [tex]$\left(x_2, y_2\right)$[/tex] internally in the ratio m: n then,

[tex]$x=\frac{m x_2+n x_1}{m+n}$[/tex] and [tex]$y=\frac{m y_2+n y_1}{m+n}$[/tex]

Here,

[tex]\left(x_1, y_1\right)=(8,-1) \\\\ \left(x_2, y_2\right)=(2,5) \\\\ (x, y)=(4, 3) \\[/tex]

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Answer:Q1. The values of a and b cannot be determined from the given information. To find the values of a and b, additional information is needed to solve the equation √2+2√3 = (a + b√6)/(2√2+√3).

Q2. To find the length and breadth of a rectangle, you need to factor the polynomial expression 6x² - 29x + 30. Then, you need to identify two numbers that multiply to 30 and add up to -29. The expression 6x² - 29x + 30 can be factored as (2x - 5)(3x - 6). The length of the rectangle is 2x - 5, and the breadth is 3x - 6. The perimeter of the rectangle is (2 * length) + (2 * breadth) = 2(2x - 5) + 2(3x - 6) = 4x + 4.

Step-by-step explanation:

Q1. The values of a and b cannot be determined from the given information. To find the values of a and b, additional information is needed to solve the equation √2+2√3 = (a + b√6)/(2√2+√3).

Q2. To find the length and breadth of a rectangle, you need to factor the polynomial expression 6x² - 29x + 30. Then, you need to identify two numbers that multiply to 30 and add up to -29. The expression 6x² - 29x + 30 can be factored as (2x - 5)(3x - 6). The length of the rectangle is 2x - 5, and the breadth is 3x - 6. The perimeter of the rectangle is (2 * length) + (2 * breadth) = 2(2x - 5) + 2(3x - 6) = 4x + 4.

Answer:     c is greater than 11

Step-by-step explanation:

Since Heather needs to spend more than $26 and she already spent $15, we can write this out as

      c + 15 is greater than 26

subtracting 15 from both sides;

     c is greater than 11

In the given expression, 7^x=28, as there is variable in one side while in other side there is constant, also there is no logarithmic value, so it is not possible to  solve the equation by changing the base of both sides

The basic formula has been changed to logb b a = [logc c a] / [logc c b]. It simply implies that to alter the base of a logarithm logb b a, we divide [log a] / [log b], where these logarithms might have any (same) positive number as a basis.

The change of base formula gives you the answer of a log with a different base by utilizing only log computations with a base of 10. The formula instructs you to divide the log of the number in parentheses by the log of your base.

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Simplifying 1/(1/4x -1/x+5) gives 4x²+20x)/5-3x

Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do.

1/(1/4x -1/x+5) = 1 ÷ 1/4x -1/x+5

= 1÷ (x+5 -4x)/4x²+20x

= 1× 4x²+20x/5-3x

= (4x²+20x)/5-3x

therefore the simplification of 1/(1/4x -1/x+5) is (4x²+20x)/5-3x

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Answer: i believe its -3x+9

Step-by-step explanation:

it is important to recognize that the minus sign in front of −(x−3) applies to both x and −3.

remove the parentheses by distributing the minus sign to the terms inside them: −2x+6−(x−3)

⇒−2x+6−x−(−3)

⇒−2x+6−x+3

combine similar terms: ⇒(−2x−x)+(6+3)

⇒−3x+9

We have a translation of 4 units downwards, so the correct graph is the first one (the one you answered).

Here we start with the parent function:

f(x) = |x|

And the translated function is:

g(x) = |x| - 4

Remember that a general vertical translation of N units of a function f(x) can be written as:

g(x) = f(x) + N

if N > 0 the translation is upwards.

if N < 0 the translation is downwards.

Here N = -4, so the translation is 4 units downwards.

Then the correct graph is exactly the one that you marked.

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The inverse meaning in math is a function or operation which reverses the order or operation of another function or operation.

Let us take an inverse math example, The inverse operation of addition is subtraction, and the inverse operation of multiplication is division.

For example, The multiplication of two numbers 3 and 6 is 3 × 6 = 18. The inverse operation of this is a division which is as follows: 18/6 = 3.

The Inverse of a Number

Consider a number y where y is not equal to zero. Then the inverse of a number y is the reciprocal of the number that is 1/y.

For example, The inverse of the number 200 is 1/200, and the inverse of the number 32 is 1/32.

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Althea volunteers 10.25 hours a week.

Given that Althea volunteers in the school library for 2 1/4 hours on Mondays, Wednesdays, and Fridays.

She volunteers 2 1/4 hours a day.

First we convert the improper fraction 2 1/4 to a proper fraction.

2 1/4 = 9/4

So by unitary method for three days the number of hours she volunteer:

3 × 9/4 = 27/4

Also, she volunteers for 1 3/4 hours on Tuesday and Thursday.

She volunteers 1 3/4 hours a day.

First we convert the improper fraction 1 3/4 to a proper fraction.

1 3/4 = 7/4

So by unitary method for two days the number of hours she volunteer:

2 × 7/4 = 14/4

So, the total number of hours Althea volunteers for a week,

27/4 + 14/4

= 41/4

= 10.25 hours

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