Use the equation y = -1/2х-3 for questions 1 and 2.
1. What is the form of this linear equation?
2.rewrite this equation in standard form.

The length of each piece of rope is 10m.

The first step is to determine the length of the rope before it was cut. In order to determine the length of the rope, multiply the length of the stick by the number of times the rope is as long as the stick.

Multiplication is the process that is used to determine the product of two or more numbers. The sign that is used to represent multiplication is x.

Length of the rope = length of the stick x 4

4 x 5 = 20m

lf the length of the rope is divided into two prices, divide the length of the rope by 2. Division is the mathematical operation that is used to determine the quotient of two or more numbers. It entails grouping a number into equal groups using another number.

Length of each piece = Length of the rope / 2

20m / 2 = 10m

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Answer:

[tex]\dfrac{20}{9}[/tex]

Step-by-step explanation:

Answer
[tex]x = \dfrac{20}{9}[/tex]. So the original number = [tex]\dfrac{20}{9}[/tex]

The original number is 20/9.

What is mean by Fraction?

A number expressed as a quotient in which a numerator is divided by denominator is called a fraction.

Given that;

The numbers are 1 5/6 and 3 2/3.

Now, Let us assume original number 'x'.

Change mixed fraction into improper fraction,

1 5/6 = 11/6

3 2/3 = 11/3

Then by the given condition,

Subtracting 7/18 from x and add 11/6, we get;

x - 7/18 + 11/6

And this is equal to = 11/3

So, we get;

x - 7/18 + 11/6 = 11/3

Add 7/18 both side,

x - 7/18 + 11/6 + 7/18 = 11/3 + 7/18

x + 11/6 = 11/3 + 7/18

Subtract 11/6 both side,

x + 11/6 - 11/6 = 11/3 + 7/18 - 11/6

x = 11/3 + 7/18 - 11/6

x = 66/18 + 7/18 - 33/18

x = 40/18

x = 20/9

Thus, The original number is 20/9.

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Answer:

Parallel: y = -4x + 23

Perpendicular: y = (1/4)x - (5/2)

Step-by-step explanation:

Parallel Line:

y = -4x + 1; (6, -1)

                  (x₁, y₁)

y - y₁ = m (x - x₁)

y - (-1) = -4 (x - 6)

y + 1 = -4 (x - 6)

y + 1 = -4x + 24

y = -4x + 23

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

Perpendicular:

y = (1/4)x + 1

y - y₁ = m (x - x₁)

y - (-1) = (1/4) (x - 6)

y + 1 = (1/4) (x - 6)

y + 1 = (1/4)x - (6/4)

    -1               -1

y = (1/4)x - (5/2)

I hope this helps!

Hello,

[tex]1) \: - 24[/tex]

[tex] 2) \frac{ - 24}{2} = - 12[/tex]

[tex] 3)\frac{ - 12}{2} = - 6[/tex]

[tex]4) \frac{ - 6}{2} = - 3[/tex]

[tex]5) \frac{ - 3}{2} = - 1.5[/tex]

Answer → -1,5

After direct variation y = 6/5 when x = 4.

So,

The initial statement is y = kx

Then to find y when x = 4.

When x = -3:

y = 3/10 × 4 ⇒ y = 6/5

Therefore, after direct variation y = 6/5 when x = 4.

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The inverse of the fuction y = 3 x + 2 is y = x/3 - 2/3.

So,

All we have to do to find the inverse of an equation is switch the variables x and y.

Now, solve for y as follows:

Therefore, the inverse of the fuction y = 3 x + 2 is y = x/3 - 2/3.

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The equation of the line y = mx + b can be used to calculate the slope of a line m = ( y₂ - y₁ ) / ( x₂ - x₁ ) that passes through two points.

A line is defined as a curve showing the shortest distance between 2 points.

Here,

The slope of the line passing through two points ( x₁, y₁ ) and ( x₂, y₂ ) is given as :

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

The line that connects two locations has the equation y = mx + b, where m is the slope of the line and b is a constant.

We can find b, using the x, y, and m values in the equation of a line to obtain the y-intercept.

Therefore, the Slope of the line can be given as m = ( y₂ - y₁ ) / ( x₂ - x₁ ) and equation of line y = mx +b.

Hence, option A is correct.

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Answer:

A or Find the slope using the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, and then substitute one point and the slope into the equation y = m x + b to find the y-intercept.

Step-by-step explanation:

The employee yearly contribution to the

U.S. Medicare tax on a salary of 40,000 $/year is $580.

Medicare is a federal employment tax that helps pay the Medicare insurance program.

The Medicare duty, occasionally known as the" sanitarium insurance duty," is a civil employment duty that contributes to the Medicare insurance program. Medicare duty, like Social Security duty, is taken from an hand's payment or paid as a tone- employment duty.

 Part A of the Medicare program, which covers sanitarium insurance for grown-ups 65 and aged, as well as persons with certain impairments or medical conditions, is funded by the Medicare duty. Medicare sanitarium insurance includes hospitalization, lodge care, nursing home care, and certain home healthcare.

Anyone working in the United States is obliged to pay Medicare levies.

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Answer:

the gfc is 1 because of the unknowns which are a and b

The value of x for the equation 4 log₃2-2 log₃x=1 is 2.30946

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which a set number, base b, must be increased in order to obtain a specific number x, is represented by the logarithm of that number.

Given,

4 log₃2-2 log₃x=1

log₃ 2⁴ - log₃ x² = 1

using logₐ(m - n) = logₐ(m/n)

log₃(2⁴ / x²) = 1

2⁴ / x² = 3¹

x = 4/√3

x = 2.30946

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Answer:

Step-by-step explanation:

yyyyyyyyyyyyyyyyyyyyyyyyyyyy

The solutions for the system of equations: x₁ ≈ - 3.967, x₂ ≈ - 0.622. (Correct choice: B)

In this question we find a system formed by one nonlinear equation and one linear equation, which can be resolved by using a graphic approach. g(x) = f(x) represents the point of intersection of the two curves. First, we plot the graphs of the two curves and, second, the point of intersection is marked on the Cartesian plane.

According to the result given by the graphing tool, there are two solutions for the system of equations: x₁ ≈ - 3.967, x₂ ≈ - 0.622.

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Answer:

C. q= -9

Step-by-step explanation:

4=q+13

-13    -13     (4-13= -9)

q=-9

hope this helps :)

The solution of the given equation 4=q+13 is -9. Thus option C is correct.

The equation is defined as an expression consisting of an equality sign.

let us consider an example  :

[tex]2x - 5 = 13.[/tex]

The given equation is:

[tex]4 = q + 13 \rightarrow 1[/tex]

For part A when q = 4 (given)

on substituting the value in equation 1 we get,

On transposing 13 to opposite side we get,

[tex]4 -13 = q[/tex]

[tex]-9 = q[/tex]

rewrite the equation as,

[tex]q =9[/tex]

The solution of the given equation [tex]4=q+13[/tex] is -9.

Thus option C is correct.

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Answer:

5x = 15

2x = 6

10x = 30

8x = 24

21x = 63

Step-by-step explanation:

The equations that can give you an answer of 3 are the following

[tex]3x=9[/tex]

[tex]6x=18[/tex]

[tex]11x=33[/tex]

[tex]10x=30[/tex]

[tex]7x=21[/tex]

The equations above are one step linear equations

and many many more

Answer:

y = - 3x - 12

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 7, 9 ) and (x₂, y₂ ) = (- 5, 3 )

m = [tex]\frac{3-9}{-5-(-7)}[/tex] = [tex]\frac{-6}{-5+7}[/tex] = [tex]\frac{-6}{2}[/tex] = - 3 , then

y = - 3x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (- 5, 3 )

3 = 15 + c ⇒ c = - 3 - 15 = - 12

y = - 3x - 12 ← equation of line

x = 5 is not an extraneous solution of the equation.

[tex](2x)^{1/2} = (x+5)^{1/2}[/tex]

Taking square on both the side of the equation, we get

[tex]((2x)^{1/2})^{2}[/tex] = [tex]((x+5)^{1/2})^{2}[/tex]

2x = x + 5

Subtracting x on both the sides of the equations, we get

2x - x = 5

x = 5

Check for Extraneous Solution by putting x = 5 in the original equation, we get

[tex](2(5))^{1/2} = (5+5)^{1/2}[/tex]

[tex]10^{1/2}[/tex] = [tex]10^{1/2}[/tex]

⇒ LHS = RHS

∴ x = 5 is not an extraneous solution of the equation.

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The solution of the given equation by rounding off it to the nearest ten-thousandth is 20716.0000.

What is a round-off of the digit?

In mathematics, a round-off is defined as an approximation of the given number to a fewer number of significant digits by taking into consideration some rules.

For eg: 13.58 ~ 13.6

Solving the given equation: 12⁴ - x = 20

We are given that 12⁴ - x = 20            —- 1

We know that 12⁴ = 20736

So, equation 1 becomes,

20736 - x = 20

x = 20736 - 20

= 20716

Hence, the solution of the given equation to the nearest ten-thousandth is 20716.0000.

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Given the radius of each sphere, the volume of sphere A and B are 33.49cm³ and 267.95cm³ respectively.

A sphere is simply a geometrical object with a three-dimensional analogue to a two-dimensional circle.

The volume of a sphere is expressed as;

V = (4/3) × π × r³

Where r is radius and π is constant pi ( π = 3.14 ).

Given the data in the question;

First, we determine the volume of sphere A.

V = (4/3) × π × r³

V = (4/3) × 3.14 × (2cm)³

V = (4/3) × 3.14 × 8cm³

V = 33.49cm³

Hence, the volume of sphere A is approximately 33.49cm³.

Next, we determine the volume of sphere B.

V = (4/3) × π × r³

V = (4/3) × 3.14 × (4cm)³

V = (4/3) × 3.14 × 64cm³

V = 267.95cm³

Hence, the volume of sphere Bis approximately 267.95cm³.

Given the radius of each sphere, the volume of sphere A and B are 33.49cm³ and 267.95cm³ respectively.

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Answer:

A and C is true statements

hope this helps :)

Step-by-step explanation:

Answer:

C and A

Step-by-step explanation:

Answer:

Its A

Step-by-step explanation:

I will answer so you can give the other person brainliest :)

Simplification of given expression is , -1

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as  .

   [tex]log_ax=N[/tex]

where, a is the base of function or equation

            x define expression

Mathematically, if   [tex]a^N=x[/tex] is an exponential function then, this can be converted to logarithmic function as   [tex]log_ax=N[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms are :

According to question,

log₃(x+1)-log₃(3 x²-3 x-6)+log₃(x-2)

applying formula of log a - log b , equation can be written as

[tex]= log_3(\frac{x+1}{3x^{2} -3x-6} ) + log_3(x-2)\\\\=log_3(\frac{x+1}{3{(x+1)(x-2)} } ) + log_3(x-2)\\\\= log_3(\frac{1}{3 {(x-2)} } ) + log_3(x-2)[/tex]

now, applying formula of log a+ log b

[tex]=log_3(\frac{1}{3{(x-2)} } (x-2)) \\\\=log_3(\frac{1}{3} )\\[/tex]

apply, [tex]log_a(\frac{1}{x}) = -log_a x[/tex]

[tex]= - log_33[/tex]

= -1

Thus, Simplification of given expression is , -1

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Check the picture below.

well, according to the line vertical test, if a vertical line anywhere on the graph hits the graph only once, then yeap, it's a function.

Answer:

81 100 121 144 169 196 225 256

17 19 21 23 25 27 29 31

Step-by-step explanation:

the formula is to square the number then subtract the preceding number in the box

The midpoint of (3,5) and (6,0) is (9/2, 5/2)

The points are given as

(3,5) and (6,0)

The midpoint of the points is calculated using

Midpoint = 1/2 * (x1 + x2, y1 + y2)

So, we have

Midpoint = 1/2 * (3 + 6, 5 + 0)

Evaluate the sum

So, we have

Midpoint = 1/2 * (9, 5)

Evaluate the product

So, we have

Midpoint = (9/2, 5/2)

Hence, the midpoint of (3,5) and (6,0) is (9/2, 5/2)

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Answer:6x-24y

Step-by-step explanation:You basically distribute the 6 with the x and the you do the same with the 4y. and thats how u get ur answer

Answer:

6x - 24y

Step-by-step explanation:

I'm guessing that they want you to distribute the 6 to each term inside the parentheses...

A solution that is real in its nature is called the real solution of that equation.

X + 5 = 0

We can solve the above equation as,

X + 5 = 0

X = -5

Now, if we plug the value of X into the equation,

X + 5 = 0

-5 + 5 = 0

0 = 0

The solution is real and is true for this equation.

While the solution of an algebraic expression solution is imaginary if it is the square root of a negative number. It involves the imaginary unit iota.

The complete solution of the expression is given below in the picture.

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Diagonal FH bisect angles EFG and EHG and the angle FEH is congruent to angle FGH.

Why is the triangle congruent?

We need to check all the statements that are applicable for the diagram.

1) EFGH is a rectangle.

The above statements is not true in general. EFGH is a quadrilateral with opposites sides are equal, it may be rectangle in some cases but it is not always be a rectangle.

2). EFGH has 4 congruent sides.

The above statement is also false. EFGH has two opposite sides are congruent.

3). Diagonal FH bisect angles EFG and EHG.

The above statement is true. Triangle EFH and FGH both are isosceles triangles and hence they both have equal angles for the equal sides. Thus, it is true in all cases.

4). Diagonal FH is perpendicular to side Fe.

The above case is not true in general.

5). Angle FEH is congruent to angle FGH.

Yes, the above statement is the correct one, because both the triangles are congruent to each other.

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The complete question is -

Triangle FGH is the image of isosceles triangle FEH after a reflection across line HF. Select all the statements that are a result of corresponding parts of congruent triangles being congruent

Sarah have $495 in her account at the end of the month.

Given,

The amount Sarah had in her bank account at the beginning of the month = $600

The deposits she made within the month = $40 and $25

The withdrawals she made = $100, $50 , $20

We have to find the balance amount in Sarah's account after all these transactions made:

The deposits Sarah had = 600 + 40 + 25 = 665

Sarah had $665 in her account in a month.

Withdrawals made by Sarah = 100 + 50 + 20 = 170

Sarah made a total withdrawal of $170 in the month.

Now, we have to find the account balance of Sarah:

Account balance = Total deposits - Total withdrawals

Account balance = 665 - 170 = 495

That is, Sarah have $495 in her account at the end of the month.

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