8th grade mathWhich quadrant is the answer to this system of equations in?A. Quadrant 1B. Quadrant 2 C. Quadrant 3D. Quadrant 4

3/7 and 5/11 are fraction when converted in decimals resulted in repeating decimals.

Repeating decimals also known as recurring decimals means after decimals , a particular digit or sequence of digits keep repeating itself indefinitely . They are non terminating numbers means which don't have a end. Bars are used over that repeating digits .

Dividing the fractions :

A . 3/7 = 0.42857

It has different values after decimals

B. 1/9 = 0.111111

it has single value 1 which is repeating itself

C . 3/4 = 0.75

two different values after decimals

D. 5/11 =  0.4545454

after decimals 45 a sequence of number is repeating itself

3/7 and 5/11 are fraction which resulted into repeating decimals.

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The equation of the line is y-8 = [tex]\frac{-4}{3}[/tex] ( x+2) .

What is equation of the line ?

    A line's coordinate plane equation can be expressed in two point form. Depending on the information at hand, a line's equation can be discovered using a variety of techniques. One approach is the two-point form. When two points that are on the line are known, this is used to find the equation of the line. The slope intercept form, intercept form, point slope form, and other crucial forms for representing the line equation.

Here the given two points are ,

[tex](x_1,y_1)=(-2,8)\\(x_2,y_2)=(7,-4)[/tex]

Now using slope formula,

slope m= [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

=> slope m = [tex]\frac{-4-8}{7+2}[/tex]

=> slope m = [tex]\frac{-12}{9}= \frac{-4}{3}[/tex]

Now using equation formula,

=> [tex]y-y_1 = m(x-x_1)\\[/tex]

=> y-8 = [tex]\frac{-4}{3}[/tex] ( x+2)

Hence the point slope form of the equation is  y-8 = [tex]\frac{-4}{3}[/tex] ( x+2) .

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Answer:

0.5

Step-by-step explanation:

-1 + 3[(10-12)³÷(-16)]

Step 1: (10 - 12)³ — Bracket

(-2)³ = -8

Step 2: -8 ÷ (-16) — Division

-8/-16

= 1/2

Step 3: 3(1/2) — Multiplication

= 3/2

Step 4: 1 + 3/2 — Addition

= 0.5

You can also type it straight into the calculator to confirm.

The average rate of change from x = -9 to x = -1 of the graph of the given function is 0.

We know that the rate of change of a function is nothing but the slope of the line.

The slope of the line is given by;

Slope = Change in y-coordinate / change in x-coordinate

We are given the graph of a function.

We need to find the average rate of change from x = -9 to x = -1.

Let us find the value of y or f(x) for the given value of x.

For x = -9, y = 2

For x = -1, y = 2.

Put the values of x and y in the slope formula, we will get;

Slope = (2 - 2) / (- 1 - (-9)) = 0

So, the rate of change of function is 0.

Thus, the average rate of change from x = -9 to x = -1 of the graph of the given function is 0.

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The perimeter of the triangle if y equals 3 feet is 31 feet.

Given:

sides of the triangle are y+5, 4y-3 and 3y+5 feet.

y = 3 feet

Let a = y + 5 = 3+5 = 8.

so a = 8 feet.

b = 4y - 3

= 4*3 - 3

= 12 - 3

b = 9 feet.

c = 3y+5

= 3*3+5

= 9+5

c = 14 feet.

Perimeter of the triangle = a+b+c

= 8 + 9 + 14

= 17 + 14

= 31 feet.

Therefore the perimeter of the triangle if y equals 3 feet is 31 feet.

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Answer: 62,110 Gallons left of icecream after his friend ate 7320 Gallons

NOT ENOUGH INFO TO PROVE HOW MUCH FRIEND HAS ENJOYED

Step-by-step explanation:

To find out how much icecream is left do

Therefore there is 62,110 gallons left of icecream

To find out how much icecream his friend has ate

Therefore his friend has ate

7320 Gallons

As AD = DB, CD bisects ∠ACD

In Δ ACD and ΔBCD

We need to prove that  CD bisects ACB

∠A = ∠B

side AC = CB (as angle A and angle B are same)

CD is ⊥ AB

So, ∠ADC = ∠BDC

By SAS  Δ ACD and ΔBCD are congurent

In congurent triangles, corresponding angles and sides are equal

So, in  Δ ACD and ΔBCD

ACD = DCB

Therefore, as AD = DB, CD bisects ∠ACD

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Explanation

Opposite sides are 5 miles each and for each semicircle we have:

Then the lenght of the track is:

Approximately 13.1416 miles

Answer:

He cannot save $5 when he is buying something instead of making it himself.

Step-by-step explanation:

He makes $10 from lawn mowing and spends $5 on Taco Bell. He has $5 left.

If he made is lunch, He would have had $10 dollars.

Andrew's argument is flawed because he is not considering all of the costs and benefits associated with his decision to go to Taco Bell instead of preparing his own meal.

An argument is a collection of claims, the premises of which are provided in support of another statement, the conclusion.

There are a few problems with Andrew's argument.

First, he is assuming that the only cost of preparing his own meal is the price of the ingredients. However, there are also opportunity costs associated with preparing his own meal, such as the time he spends making it and the opportunity to do something else during that time (such as study for his exam).

Second, Andrew is assuming that he would have spent the same amount of money on ingredients as he did on his meal at Taco Bell. However, it is possible that the ingredients he would have used to make his own meal would have cost less than $5, in which case he would not have saved as much money as he thinks.

Finally, Andrew is assuming that he would have spent the same amount of time preparing his own meal as he did going to Taco Bell. However, it is possible that it would have taken him longer to prepare his own meal, in which case the opportunity cost of his time would have been even higher.

Overall, Andrew's argument is flawed because he does not evaluate all of the expenses and advantages of his decision to eat at Taco Bell instead of cooking his own dinner.

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Step 1. The party will be thrown by Steve, Jo, Lucy, Max, and Alex --> 5 people.

On Monday, each invites 3 friends. So for, the number of people invited is:

Step 2. On Tuesday, the friends that were invited (15) invited 3 more people each. The number of people invited now is:

Step 3. On Wednesday, the 45 people invited on Tuesday, each invite 3 more people. The number of people invited again multiplies by 3:

Step 4. The trend continues so for Thursday, the number of people invited on the previous day multiplies by 3:

Step 5. On Friday the number of people invited is:

Step 6. Finally, on Saturday, the day of the party, the number of people invited is multiplied one last time by 3:

Answer:

3,645

The equations of the lines that pass through the point (0,5) and intersect the circle at exactly one point are y = 4/3x + 5 and y = -4/3x + 5.

The equation of a circle centred at the origin with a radius of 3 units is defined by x² + y² = 3². The coordinates of the point are (0, 5). Let the equation of the tangent be y = mx + c.

y = mx + c

5 = m(0) + c

c = 5

The equation of the tangent is of the form mx -y + 5 = 0. The distance of the centre of the circle from the tangent must be equal to the radius of the circle.

d = |ax + by + c|/√(a² + b²)

3 = |m(0) + (-1)(0) + 5|/√[m² + (-1)²]

√[m² + (-1)²] = 5/3

m² + 1 = 25/9

m² = 16/9

m = ±4/3

The equations of the tangents are y = 4/3x + 5 and y = -4/3x + 5.

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10)

we get the points from the table are (2,12) and (8,0).

Consider the line equation.

where b is the y=intercept.

Substitute x=2 and y=12, we get

Substitute x=8 and y=0 in the line equation, we get

Substitute m value in this equation to find the value of b.

Dividing both sides by 3, we get

Hence the y-intercept is 16.

11)

we get the points from the table are (2,-5) and (4,17).

Consider the liner function.

where b is the y-intercept.

Substitute x=2 and y=-5, we get

Substitute x=4 and y=17 in the equation, we get

Substitute the value of m in this equation to find the value of b.

Hence the y-intercept is -27.

Answer:

z = -3.2

Step-by-step explanation:

-1.25(z + 8) = -6

-1.25z - 10 = -6

           +10   +10

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

-1.25z = 4

÷(-1.25) ÷(-1.25)

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

z = -3.2

I hope this helps!

Answer

Explanation

The distributive property tells us that:

Thus, we can apply this property to our given equation in the right side:

You have the following inequality:

√x > 2

Consider that only positive values of x result in real solutions. Moreover, if you squared both sides of the inequality, you obtain:

x > 4

The graph of the inequality is shown below:

For solving this problem we have to know the transformations between feeds and kilometers and seconds to hours:

Now we can make the transformation:

Answer:

plug the the x values in the chart into the formula one at a time and plug it into a calculator to get your y values.

example: y= -3/5(10)-3 —-> -9 y value

Step-by-step explanation:

For the information given in the statement let:

*C the million metric tons of rice that China produces per year

*P the million metric tons of rice that Philippines produces per year

So, you have

Therefore, annually China produces 12.25 times the amount of rice that the Philippines produces.

Answer:

12.25 times

Step-by-step explanation:

196/16 = 12.25

Trigonal pyramidal is the NH3 molecule's molecular shape. The hydrogen atoms are attracted to the lone pair of electrons on the nitrogen atom, which causes the NH3 bond angle to be 107 degrees.

The process of merging two atomic orbitals to produce a new variety of hybridized orbitals is described as hybridization.

Usually, this mixing creates hybrid orbitals with entirely distinct energies, forms, and other characteristics.

Atomic orbitals with the same energy level are principally responsible for hybridization.

However, if the energies of the orbitals are equivalent, the process can involve both fully filled and partially filled orbitals.

We can better understand bond formation, bond energies, and bond lengths by using the hybridization concept, which is an extension of valence bond theory.

Hence, Trigonal pyramidal is the NH3 molecule's molecular shape. The hydrogen atoms are attracted to the lone pair of electrons on the nitrogen atom, which causes the NH3 bond angle to be 107 degrees.

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Okay, here we have this:

Considering the provided information, we are going to calculate the requested composition and time, so we obtain the following:

Composite function N(T(t)):

Finally we obtain that N(T(t)) is equal to 972t^2-379.2t-119.47.

Now, let's the time when the bacterias count reaches 26087:

To find how many picture are in the yearbook, multiply the number of pages of the yearbook by the number of pictures on one page. This is 32 times 8:

There are 256 picture in the yearbook.

The mean mark of the girls is 86.

You must first add up all the numbers (3 + 11 + 4 + 6 + 8 + 9 + 6 = 47) before you can determine the mean. The amount is then divided by the number of scores utilized (47 / 7 = 6.7).

Given information:

The number of total students in the class is 30

Given number of boys in the class is 20

Then, the number of girls will be = 30-20

=10

The mean mark of the class = 70×30

= 2100

The guy's average grade is = 62.

Then, mark for the boys = 62×20

= 1240

The mark for the girls = 2100-1240

= 860

Then the mean mark of the girls will be  =860/10

= 86

Hence, the mean mark for the girls is 86

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The x-coordinates of the points of intersection of the given function graphs are;

1) x = 0 and x = 2

2) x = -1

3) x = 0

The point of intersection of a graph is defined as the point or coordinates where two lines or curves meet each other.

1) In the first graph, we are given the functions as;

f(x) = -³/₄x² + 3x + 1

g(x) = 2ˣ

Thus;

From the graph, f(x) = g(x) is at (2,4 and (0, 1)

2) In the first graph, we are given the functions as;

f(x) = x² + 4x + 2

g(x) = (¹/₂)ˣ + 1

Thus;

From the graph, f(x) = g(x) is at (-1. 3)

C) In the third graph, we are given the functions as;

f(x) = -⁷/₃x - 3

g(x) = 2ˣ - 4

Thus;

From the graph, f(x) = g(x) is at (0, -3)

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Solution:

Given the ordered pairs;

The domain, x, of the function is;

Then, the range, y, is;

The resultant answer to the given inequality is x ≤ -5/12 and the graph of the answer is shown.

So, solve the inequality as:

Now, plot x ≤ -5/12 on the graph as follows:

Therefore, the resultant answer to the given inequality is x ≤ -5/12 and the graph of the answer is shown.

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The linear approximation of the function is given by a³ - 3a² +4 + 10ax

The given function is f(x)=x³+5x²+4

Let us find the linear approximation.

L(a) = f(a) + f'(a)(x-a)

let us differentiate the function

f'(x) = 2x²+10x

Let us find the value of the function at the exact point a

f'(a) = 2a²+10a

f(a) = a³+5a²+4

L(a) = f(a) + f'(a)(x-a)

L(a) = a³ + 5a² + 4 + 2a² + 10a (x-a)

L(a) = a³ + 7a² +4 + 10ax - 10a²

L(a) = a³ - 3a² +4 + 10ax

The use of a line to approximate the value of a function at a point is the definition of a linear approximation of either a function. When we see a curve (of a function) and a point on it, we immediately think of the tangent line concept.

If the equation of the tangent line is discovered at the supplied point, one can roughly calculate the value of something similar to the function at every location that is very close to the supplied point using the equation of the tangent line. This concept is also known as the tangent line approximation because the tangent line is utilized. Additionally called linear approximation.

Therefore the linear approximation of the function is given by

a³ - 3a² +4 + 10ax .

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The given function is:

Differentiate w. r. t. z to get:

Hence the derivative is 9cot9z.

If the high temperature on Friday is equal to this week's average daily high temperature, the option that could be Friday's high temperature is: C. -12°.

Using this formula to find the high temperature

High temperature= Last week average daily high temperature + ( -This week average daily high temperature)

Let plug in the formula

High temperature = 12° + (-24°)

High temperature= -12°

Therefore the correct option is C.

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The slope of the given linear function is found as -3/4.

For the given question, the values for the x and y coordinates are given .

Consider two points;

(x1, y1) = (4, 6)

(x2, y2) = (8, 3)

Slope = m = (y2 - y1)/(x2 - x1)

Put the values.

m = (3 - 6)/(8 - 4)

m = -3/4

Thus, the slope of the given linear function is found as -3/4.

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Answer;

It causes an increase in the MAD, but not the IQR

Explanation;

Mathematically, we know that an outlier in a dataset represents a value that is at least 2 standard deviations away from the mean value

While MAD represents the mean absolute deviation, IQR represents the interquartile range

It is expected that the outlier affects the value of the standard deviation

By calculating the MAD, we have to subtract values from the mean and square them and this makes the mean absolute deviation affected by the outlier

Hence, we can conclude that the presence of an outlier increases the mean absolute deviation

For the interquartile range, it only moves the lower quartile and the upper quartile same way and thus, it has no effect on it