If x and y vary directly and x=25 when y=100 find x when y=24.
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The statement "If a ≥ 0, then |a| = -a" is always false.

What is the absolute value?

Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.

The absolute value of a real number, denoted by |a|, is the non-negative value of a without regard to its sign.

Therefore, if a is greater than or equal to zero, the absolute value of a is equal to itself.

On the other hand, -a is the negative of a, which is only the case when a is less than zero.

Hence, |a| can never equal to -a when a ≥ 0, because the absolute value is always non-negative, while -a is always negative.

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The sentence "If a 0, then |a| = -a" is untrue at all times. 4 is equal to 4 in absolute terms. The formal notation for a number's absolute value is |x|.

Without taking direction into account, absolute value describes how far away from zero a certain number is on the number line. A number can never have a negative absolute value. The non-negative value of a, indicated by the symbol |a|, is the absolute value of a real number, regardless of its sign. It follows that if an is higher than or equal to zero, its absolute value is also zero.

However, -a is the opposite of a, and is only true when an is less than zero. This means that when an is greater than 0, |a| can never equal -a because the absolute value is always non-negative whereas -a is always negative. Without taking direction into account, absolute value describes how far away from zero a certain number is on the number line.

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Answer:

x=1

Step-by-step explanation:

The roots of the equation 25x² + 60x + 37 = 0 in simplest form will be - 6/5 + 100i and - 6/5 - 100i.

Let the equation be ax² + bx + c = 0.

Then the roots of the equation will be

[tex]\rm x = \dfrac{-b \pm \sqrt{b^2 - 4 a c }}{2a}[/tex]

The equation is given below.

25x² + 60x + 37 = 0

The roots of the equation is given as,

x = [- 60 ± √{(60)² - 4 × 25 × 37}] / (2 × 25)

x = [- 60 ± √(-100)] / 50

x = [- 60 ± 100i] / 50

x = - 6/5 ± 100 i

x = - 6/5 + 100i, - 6/5 - 100i

The roots of the equation 25x² + 60x + 37 = 0 in simplest form will be - 6/5 + 100i and - 6/5 - 100i.

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The equations that form the system that models this situation are:

B. x² = y + 16  

F. 4y - 1 = 7x

The solution of the system of equations is: A. (5, 9).

In this scenario, the relationship between two numbers, where x represents the first number and y represents the second number is given by the following word description:

"The square of the first number is equal to the sum of the second number and 16."

"The difference of 4 times the second number and 1 is equal to the first number multiplied by 7."

Next, we would translate the word problem into an algebraic equation:

x² = y + 16    .......equation 1.

4y - 1 = 7x      .......equation 2.

Next, we would use an online graphing calculator to plot the given system of equations in order to determine its solution.

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The number of guitarist who plays classical solos in the contest is 30.

Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.

The ratio of a and b is denoted as a : b.

Given that,

Total number of musicians entered in the contest = 64

5/8 of these musicians are guitarists.

Number of guitarists = (5/8) × 64 = 40

Also we have,

Ratio of number of guitarists playing jazz solos to the total number of guitarists = 1 : 4 = 1/4

That is, of the 4 guitarists, 1 is a guitarist playing jazz solos.

Multiplying both numerator and denominator with 10, 1/4 = 10/40

So of the 40 guitarists, 10 number of guitarists play jazz solos.

Number of guitarists who play classical solos = 40 - 10 = 30

Hence 30 guitarists play classical solos.

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Answer: 90

Step-by-step explanation: I multiplied 18 by 5

Answer:

H=90

Step-by-step explanation:

if H÷5=18, then reverse it. so 18×5=90

The exponential form of 10 * 10 is [tex]10^{2}[/tex] . We get it from the prime factorization.

In order to get the exponential form of a number we have to write the prime factorization of that number. Prime factorization of the number is that number written as a product of prime numbers or as a product of powers of prime numbers. A basic exponential function from its definition is of the form f(x) = b x, where 'b' is a constant and 'x' is a variable. generally it refers to the positive valued function of a real variable. We can find the prime factorization of a number using factor trees, which are tools used to repeatedly break a number into products until all of the factors are prime numbers.

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The number of zeros in a polynomial equation is determined by the number of degrees it has, which is n.

Polynomial

A polynomial is a mathematical equation made up of variables, constants, and exponents that are mixed using addition, subtraction, multiplication, and division.

Bi-quadratic Polynomial

(Not comparable) Biquadratic (mathematics) x4 + 3x2 + 2 is an example of a polynomial expression that only uses a variable's zeroth, second, and fourth powers. When used in the form x4 4x3 + 3x2 x + 1, it is sometimes extended to any expression containing the biquadrate or fourth power (but not higher powers).

What is a Polynomial Equation?

Polynomial equations are those created by combining variables, exponents, and coefficients. The greater of its possible exponents is referred to as the equation's degree.

Among all possibilities, the linear polynomial p(x) = 2x+3 is a polynomial of degree 1. Consequently, there is just one zero in it.

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The factoring method for the polynomial x²+6x-16 is to find the values that satisfies the equation.

The given polynomial is x²+6x-16.

Now, in order to factorize the polynomial, we have to think of any two number such that by adding them the sum comes out to be 6 and when we multiply them, there product is -16, this is the factoring method for this polynomial.

So, by hidden trial method, we can analyze that there are two numbers 8 and -2.

By adding them, they becomes 6 and on multiplying they become -16.

So, the factorized form of the polynomial will be,

(x-8)(x+2)

Hence, the polynomial was factorized.

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The solution to the given system of linear equations is x = -4, y = -10

From the question, we are to solve the given system of linear equations.

The given system of linear equations is

y = 2x - 2          ------------ (1)

-4x - y = 26     ------------ (2)

Substitute equation (1) into equation (2)

-4x - y = 26

-4x - (2x - 2) = 26

- 4x - 2x + 2 = 26

-6x + 2 = 26

-6x = 26 - 2

-6x = 24

x = 24/-6

x = -4

Substitute the value x into equation (1)

y = 2(-4) - 2

y = -8 - 2

y = -10

Hence, the x = -4, and y = -10

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Answer:

lo l oh my gosh hi i havent seen u in so many years

Step-by-step explanation:

The solution to the equation 6y - 2(y + 1) = 3(y - 2) 6 is y = -34. So, the correct answer to the question is a. y = -10.

What is algebraic equation ?

An algebraic equation is a mathematical statement that asserts the equality of two expressions, each of which is made up of numbers and/or variables. The expressions are separated by an equal sign (=). The goal of solving an algebraic equation is to find the value(s) of the variable(s) that make the equation a true statement.

To find the solution to the equation 6y - 2(y + 1) = 3(y - 2) 6, we must first simplify both sides of the equation by following the order of operations (PEMDAS). First, we simplify the right side of the equation: 3(y - 2) 6 = 3y - 6 * 6 = 3y - 36. Next, we simplify the left side of the equation: 6y - 2(y + 1) = 6y - 2y - 2 = 4y - 2.

Now we have the equation: 4y - 2 = 3y - 36

Next, we can add 2 to both sides of the equation and get: 4y = 3y - 34

Finally we subtract 3y from both sides of the equation and get: y = -34

Therefore, the solution to the equation 6y - 2(y + 1) = 3(y - 2) 6 is y = -34. So, the correct answer to the question is a. y = -10.

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In order to find the y− intercept of a parabola in factored form, plug in 0 for x and find the corresponding y− value

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The algebraic expression in question b can be simplified to give (x² - 5x)/5.

Simplification of an algebraic expressions is the process of writing an expression in the most efficient and compact way, that is in their simplest form, without changing the value of the original expression.

2x²(x - 5)/10x = 2x × x(x - 5)/ 2x × 5

2x is a common factor to both the numerator and denominator, hence can cancel out

2x²(x - 5)/10x = x(x - 5)/5

opening bracket we have;

2x²(x - 5)/10x = (x² - 5x)/5

Therefore, (x² - 5x)/5 is the result after simplifying the algebraic expression 2x²(x - 5)/10x

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Answer:

210 minutes a week

Step-by-step explanation:

840 minutes/4 weeks

The slope of -10 as calculated from the data given is found out to be as 0.

Let's say y = -1= ,

Now, we know that the formula to calculate slope is y = mx+ b y .

This is known as slope-intercept form and can be written as ,

y = m x + b,

m = slope and b b= y-intercept.

y = mx +b y

y  = m x + b

Therefore , by looking at this formula we can say that the value of m is 0 .

So , the slope is found out to be 0.

The slope is defined as the change in y coordinate with respect to the change in x coordinate of that line.

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In the equation, r will have the value 1.79.

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. The sign shows the relationship of equality between the expression written on the left side with the expression written on the right side.

14.3 = pi (r²) (1.4)

(r²) = 14.3/pi(1.4)

where pi = 3.142

(r²) = 14.3/3.142(1.4)

(r²) = 14.3/4.3988

(r²) = 3.212

r = √3.212

r = 1.79

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Answer:

the answer is 4

2+2=4 bc 1+1 is 2 ×2 and that is 4 your welcome

Answer:

9 and 10

Step-by-step explanation:

66 divided by 7 would be 9.4 which lies between 9 and 10.

The area of a triangle with sides 3 cm, 4 cm, and 5 cm is 6 cm² using Heron's formula.

Step 1: First, calculate the semi-perimeter of the triangle by adding the three sides of the triangle together and dividing by 2. In this case, the semi-perimeter would be (3 + 4 + 5) / 2 = 6 cm.

Step 2: Next, use the semi-perimeter and the three side lengths of the triangle to calculate the area. The formula for Heron's formula is:

Area = √(s(s-a)(s-b)(s-c))

Where s is the semi-perimeter, and a, b, and c are the three sides of the triangle.

So, plug in the values,

Area = √(6(6-3)(6-4)(6-5))

Area = √(632×1)

Area = √(36)

Area = 6 cm²

Therefore, the area of the triangle is 6 cm²

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Area of the triangle DEF = 35 square unit.

A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.

Given,

Vertices of triangle

D(4, -3), E(-2, 1), and F(-9. -6)

   x₁  y₁      x₂ y₂              x₃ y₃

Area of triangle S = 1/2[x₁(y₂−y₃)+x₂(y₃−y₁)+x₃(y₁−y₂)]

Area of triangle DEF = 1/2[4(1 - -6) + -2(-6 - -3) + -9(-3 - 1)]

                                  = 1/2 [4(7) -2(-3) -9 (-4)]

                                  = 1/2[28 + 6 + 36]

                                  = (1/2) (70)

Area of triangle DEF = 35 square unit

Hence, 35 square unit is the area of triangle DEF.

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The required graph is attached below.

A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates,

Given here: The points (0,-2) (-1,2) Also the given equation is

y=-4x-4+2

y=-4x-2

Thus this is linear graph with y intercept at -2 and using the equation we plot the two points from Table 2.

Hence, The points are plotted.

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Total 24 minutes, x, will it take before the balloon has shrunk to a diameter of 8 feet.

In the given question, we have to find how many minute, x, will it take before the balloon has shrunk to a diameter of 8 feet.

From the given question, a hot-air balloon has a 14-foot diameter.

Hot-air balloon is being deflated at a rate of 0.25 feet per minute.

So the slope will be = -0.25, the negative sign is there because hot-air balloon is being deflated.

Let the amount of air left in the hot-air balloon at time n minutes is A(n) feet diameter.

The initial value of A(n) is 14-foot diameter.

Thus when n = 0, the value A(n) will be 14.

So, we can write the relation as

A(n) = -0.25n + 14

We need to find the amount left after x minute. So n = x.

The balloon has shrunk to a diameter of 8 feet. So A(n) = 8 feet

Now the equation is

8 = -0.25x + 14

Subtract 14 on both side, we get

-0.25x = -6

Divide by -0.25 on both side, we get

x = 24

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The complete question is:

A hot-air balloon has a 14-foot diameter that is being deflated at a rate of 0.25 feet per minute. How many minutes, x, will it take before the balloon has shrunk to a diameter of 8 feet?

Answer:

x=4, y=3. (4, 3).

Step-by-step explanation:

-3y=-2x-1

y=x-1

--------------

-3(x-1)=-2x-1

-3x+3=-2x-1

-3x-(-2x)+3=-1

-3x+2x=-1-3

-x=-4

x=4

y=4-1=3

the slope of the line is 8 and equation line is y = 8x.

What is the slope of line?

Given two line-side coordinates, use the slope formula to determine the slope of the line. The slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations. Whichever point you choose to classify as the first and which as the second doesn't matter.

We know that formula two find the slope of the line joining two points which is

slope m = 24-16 / 3-2

m = 8/1 = 8

y = 8x

Hence the slope of the line is 8 and equation line is y = 8x.

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