5. Noah is solving an equation and one of his moves is unacceptable. Hereare the moves he made. Which answer best explains why the "divide eachside by x step is unacceptable? *2(3+6) - 4= 8 + 6321 + 12 - 4= 8 + 612.1 + 8 = 8 + 6.120 = 602 = 6original equationapply the distributive propertycombine like termssubtract 8 from both sidesdivide each side by IO When you divide both sides of 2x = 6x by x you get 2x^2 = 6x^2.When you divide both sides of 2x = 6x by x it could lead us to think that there is nosolution while in fact the solution is x = 0..aWhen you divide both sides of 2x = 6x by x you get 2 = 6x.aOWhen you divide both sides of 2x = 6x by x it could lead us to think that there is nosolution while in fact the solution is x = 3..

Inverse proportionality is when the value of one quantity increases with respect to a decrease in another, they behave opposite in nature.

It is represented by the following expression:

Since P=24 when Q=3, we can substitute and solve for the constant k:

Then, the equation that represents the inverse variation would be:

The most appropriate choice for area of rectangle will be given by -

Area of classroom = [tex]4\frac{27}{40}[/tex] [tex]m^2[/tex]

What is area of rectangle?

Rectangle is a four sided figure whose parallel sides are equal and whose every angle is 90°

The total space taken by the rectangle is called area of the rectangle.

If the length of the rectangle be l and the breadth of the rectangle be b, then area of the rectangle is given by

Area = [tex]l \times b[/tex]

Here,

Length of classroom = [tex]6\frac{4}{5}[/tex] m = [tex]\frac{34}{5}[/tex] m

Width of classroom = [tex]1\frac{3}{8}[/tex] m = [tex]\frac{11}{8}[/tex] m

Area of classroom = [tex]\frac{34}{5} \times \frac{11}{8}[/tex]

                               = [tex]\frac{187}{40}[/tex]

                               = [tex]4\frac{27}{40}[/tex] [tex]m^2[/tex]

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Answer:

The first option is correct

Explanation:

Two negatives makes a positive.

Solution

We have the following expression:

Here we have 3 terms:

Variable terms:

Constant term

Elimination Method : In the elimination method you either add or subtract the equations to get an equation in one variable. When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.

The given system of equation :

x - y = 5 ( 1 )

- x - y = - 11 ( 2 )

Add the equation ( 1 ) & ( 2 )

x - y + ( -x - y ) = 5 + ( -11 )

x - y -x - y = 5 - 11

x - x - y - y = -6

0 - 2y = - 6

y = -6/( -2)

y = 3

Substitute the value of y = 3 in the equation ( 1)

x - y = 5

x - 3 = 5

x = 5 + 3

x = 8

Answer : x = 8, y = 3

Explanation

The question wants us to obtain the margin of error

A margin of error tells you how many percentages points your results will differ from the real population value.

The formula to be used is

To do so, we will have to list out the parameters to be used

The next step will be to find the z-score value for a confidence level of 80%.

From the statistical table, we have

So, we can input the given data obtained into the formula

So we will have

So the margin of error (M.E.) = 4.163 (To 3 decimal places)

In triangle PQR

Construction: Draw PX perpendicular to QR where x lies on QR

Since:

PX perpendicular to QR

In the 2 triangles PXQ and PXR

given

proved up

PX = PX ------- common side in the 2 triangles

Triangle PXQ congruent to triangle PXR by the AAS theorem of congruency

As a result of congruency

PQ = PR ------- proved

We will have the following:

So, the value of x is 8.

Explanation:

If 'x' is the amount each owner will pay, there are 8 owners and the total amount to pay is $5,400 the equation to solve is:

Solving for x:

Answer:

Each owner has to pay $675

Answer:

Step-by-step explanation:

Dimensions of the framed photograph are:

Area of the framed photograph is:

The frequency of middle C = 262 Hz

The formula for calculating the frequency, F hertz, of a note n seminotes above the concert pitch is:

This can be re-written as:

Middle C is 9 semitones below the concert pitch

That is, n = -9

To find the frequency of middle C, substitute n = -9 into the equation for F

The frequency of middle C = 262 Hz

the length of a rectangle is 11 yd more than twice the width and the area of the rectangle is 63 yd squared. find the dimensions of the rectangle.​

Let

L ------> the lenght

W ----> the width

we know that

the area of rectangle is

A=L*W

A=63 yd2

63=L*W -------> equation 1

and

L=2W+11 ------> equation 2

substitute equation 2 in equation 1

63=(2W+11)*w

2W^2+11w-63=0

solve the quadratic equation using the formula

a=2

b=11

c=-63

substitute

the solutions for W are

w=3.5 and w=-9 (is not a solution, because is negative)

so

Find the value of L

L=2W+11 -------> L=2(3.5)+11

L=18

therefore

the dimensions are

Hello!

In a sample of 1100 people, the specific candidate got 624 votes. So, we can write it as 624/1100.

And if the total of voters is 40,000, how many votes this specific candidate will receive? We can write it as x/40,000.

Now, let's equal both fractions look:

Approximately 22691 votes.

The slope intercept form of a line can be expressed as,

Here, m is the slope of the line and c is the y intercept.

Comparing the above equation with the given equation of a line y=-5x+2, we get

m=-5.

The slope of a line perpendicular to line with slope m is -1/m.

Hence, the slope of line perpendicular to y=-5x+2 is,

The new line is given to be passing through point with coordinates (x1, y1)=(3, -1).

The point slope form of a line passing through point with coordinates (x1, y1)=(3, -1) and having slope m1 is,

Therefore, the slope-intercept form of the equation of the line perpendicular to y = -5x + 2 and passing through (3,-1) is,

Answer:

• The dimensions of the garden are 90 feet by 60 feet.

• The length of the garden is 90 feet.

Explanation:

Let the length of the garden = l

The width is exactly two-thirds of the length, Width = (2/3)l

If 300 feet of antique picket fencing are to be used to enclose the garden, this means that the perimeter of the proposed garden is 300 feet.

Next, solve the equation for the length, l:

The length of the garden is 90 feet.

Next, we determine the width.

The dimensions of the garden are 90 feet by 60 feet.

Given:

point (8,8).

slope 11/6

The slope intercept form is,

where m is the slope and b is the y-intercept.

we know that m=11/6 so subistute in the equation.

Now, let us plug in the point in the equation to find the value of b that is the y-intercept.

If Earl Miller, a customer of J. Crew, will pay $400 for a new jacket. J. Crew has a 60% markup on selling price. The most that J. Crew can pay for this jacket is $160.

Given parameters:

Cost of new jacket = $400

Markup = 60%

Now let find the amount that was paid for the jacket using this formula

Amount = Cost of new jacket × ( 1- markup)

Let plug in the formula

Amount = $400 × ( 1 - .60 )

Amount = $400 × .40

Amount = $160

Therefore we can conclude that the amount of $160 was paid the most.

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By using the completing the square method, f(x) = x² − 8x + 3 in vertex form is: B. f(x) = (x − 4)² − 13.

In this exercise, you're required to rewrite the given function in vertex form by using the completing the square method. Mathematically, the vertex form of a quadratic equation is given by this formula:

y = a(x - h)² + k

Where:

h and k represents the vertex of the graph.

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

f(x) = x² − 8x + 3

f(x) = x² − 8x + (8/2)² - 13

f(x) = x² − 8x + (4)² - 13

f(x) = x² − 8x + 16 - 13

f(x) = (x² − 8x + 16) - 13

f(x) = (x − 4)² − 13

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ANSWER

y = -7

EXPLANATION

To solve using the substitution method we have to clear x from one of the equations as a function of y. For example, for equation 2:

Then replace x in the first equation by this expression:

And solve for y:

Explanation

Given the following expression

SOLUTION

Given the question in the question tab, the following are the solution steps to answer the question.

STEP 1: Write the formula for calculating compound amount

where

A = final compounded amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

STEP 2: Write the given data

Semiannually means that n will be 2

STEP 3: Calculate the compound amount

Hence, the compounded amount after 4 years is $18,748.1972

SOLUTION

The questions is outside scope

Given:

The temperature in Baguio is 18.6℃.

The temperature in manila is 31.5℃.

To find:

The differene bin temperature etween imanila and aguio.

Explanation:

The difference between manila and Baguio's temperature s

Thus, manila is 12.9 degrees Celcius warmer than Baguio.

Final answer:

anila is 12.9 degrees Celcius warmer than Baguio.

ANSWER

EXPLANATION

The equation of a circle is given by:

where (h, k) = center of the circle

r = radius of the circle

The center of a circle is the midpoint of the endpoints of the diameter of the circle. Hence, to find the center of the circle, we have to find the midpoint of the diameter:

where (x1, y1) and (x2, y2) are the endpoints of the diameter.

Hence, the center of the circle is:

To find the radius of the circle, we have to find the distance between any endpoint of the circle and the center of the circle.

To do this apply the formula for distance between two points:

Therefore, the radius of the circle is:

Hence, the equation of the circle is:

The quadrants of a coordinate plane are:

Then, we can say that the rectangle PQRS is in the first quadrant.

17.86 seconds

The starting point of the elevator car = 27 feet above the ground

The endpoint point of the elevator car = 102 feet above the ground

The total distance traveled by the elevator car = 102 feet - 27 feet

The total distance traveled by the elevator car = 75 feet

Time taken by the elevator car to rise 4.2 feet = 1 second

Time taken by the elevator car to rise 75 feet = 75/4.2 seconds

Time taken by the elevator car to rise 75 feet = 17.86 seconds

Therefore, it takes the car 17.86 seconds to reach a height of 102 feet above the ground

To detrmine the formula of the polynomial, we check for the roots on the graph:

when y = 0, x = -2

when y = 0, x = 4

We have two roots.

x = -2

x + 2 = 0

x = 4

x - 4 = 0

3rd factor is x = 0

Hence, we have two factors: x(x + 2) and (x - 4)

The polynomial function using the factors:

Next, we find the value of a:

To get a , we pick a point on the graph. let the point be (0, -4)

substitute the point in the function above:

The formula of the polynomial becomes:

Determine the product of two expressions.

So answer is,

To find the solution of the system by graphing we need to plot each line in the plane and look for the intersection.

First we need to write both equations in terms of y:

now we need to find two points for each of this lines. To do this we give values to the variable x and find y.

For the equation 2x-y=-1, if x=0 then:

so we have the point (0,1).

If x=1, then:

so we have the point (1,3).

Now we plot this points on the plane and join them with a straight line.

Now we look for two points of the second equation.

If x=0, then:

so we have the point (0,-3)

If x=1, then:

so we have the point (1,-1).

We plot the points and join them wiith a line, then we have:

once we have both lines in the plane we look for the intersection. In this case we notice that the lines are parallel; this means that they wont intersect.

Therefore the system of equations has no solutions.