Solve graphically the system of linear equations: 3x−2y=6 3x+10y=−12


Please help me

Replace x in each equation with 4:

f(x) = x^2 +2x-3 = 4^2 + 2(4) -3 = 16 + 8 -3 = 21

g(x) = x^2-9 = 4^2 -9 = 16-9 =7

Now you have values for f(x) and g(x) now you can solve for f/g and f+g:

f/g = 21 / 7 = 3

f+g = 21 + 7 = 28

For this case, we have that by definition:

[tex](f + g) (x) = f (x) + g (x)\\(\frac {f} {g})(x) = \frac {f (x)} {g (x)}[/tex]

We have the following functions:

[tex]f (x) = x ^ 2 + 2x-3\\g (x) = x ^ 2-9[/tex]

So:

[tex](f + g) (x) = x ^ 2 + 2x-3 (x ^ 2-9)\\(f + g) (x) = x ^ 2 + 2x-3 x ^ 2-9\\(f + g) (x) = 2x ^ 2 + 2x-12\\(f + g) (4) = 2 (4) ^ 2 + 2 (4) -12\\(f + g) (4) = 2 * 16 + 8-12\\(f + g) = 32 + 8-12\\(f + g) (4) = 28[/tex]

On the other hand:

[tex](\frac {f (x)} {g (x)}) = \frac {x ^ 2 + 2x-3} {x ^ 2-9}\\Evaluated\ at\ x = 4[/tex]

[tex](\frac {f (x)} {g (x)}) = \frac {4 ^ 2 + 2 (4) -3} {4 ^ 2-9} = \frac {16 + 8-3} {16 -9} = \frac {21} {7} = 3[/tex]

Answer:

[tex](f + g) (4) = 28\\(\frac {f} {g}(4)) = 3[/tex]

-4/3 is the nth term

Answer:

5 cups 39 fl oz

Step-by-step explanation:

There are 2 cups to a pint, so 2pt 4 fl oz becomes 4 cups 4 fl oz, which is less than 5 cups 39 fl oz

Answer:

A=3x^2+5x-6

B=-2x^2-6x+7

A-B=(3x^2+5x-6)-(-2x^2-6x+7)

remove parentheses

A-B=3x^2+5x-6+2x^2+6x-7

combine like terms

A-B=5x^2+11x-13

Answer:

23

46

99

1/3

1/2

7/8

Step-by-step explanation:

Let's find out by writing out each of the numbers.

17 = Seventeen (Seventeen stands alone)

20 = Twenty (Twenty stands alone)

23 = Twenty-three will be hyphenated

46 = Forty-six will be hyphenated

99 = Ninety-nine will be hyphenated

1/3 = one-third will be hyphenated

1/2 = one-half will be hyphenated

7/8 = seven-eights will be hyphenated

Now we ask ourselves why are they hyphenated?

We hyphenate because we need the two words to be glued together to show readers that the two or more elements of a sentence are link to each other.

Answer:

23

46

99

1/3

1/2

7/8

Answer:

the first one i believe

Step-by-step explanation:

hope this helps

Answer:

3√4

Step-by-step explanation:

Answer:  16

Step-by-step explanation:

[tex]64^{\frac{2}{3}}=(2^6)^{\frac{2}{3}}=2^{\frac{12}{3}}=2^4=\boxed{16}[/tex]

Answer:

Step-by-step explanation:

If breadth =x

length =x+2

Area =length *breadth

Area =x(x+2)=80

X^2+2x-80=0

X^2 +10x - 8x - 80=0

X(x+10)- 8(x+10)=0

(X-8)(x+10)=0

X=8 or x=-10

X=8(since breadth cannot be a negative value x cannot be negative)

My life is not linear. Time is not constant. My life (and time included) is just a series of times that do not run parallel to each other. Instead, they drift further or closer as a function of velocity and curvature of space time.

Answer: If you are looking for a linear equation in your life, an example could be the rate of the grass growing in your lawn. The y axis could be the height and the x axis could be the time. As it grows, the line representing the grass could go up gradually; when you cut it, the line can stop. Keep doing that for however long you'd like to represent the grass growing/getting cut.

Answer: [tex]y=-2x-3[/tex]

Step-by-step explanation:

The equation of the line in slope-intercept form, is:

[tex]y=mx+b[/tex]

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

By definition, parallel lines have the same slope.

Then:

- Find the slope of the the line that connects the points (-7,3) and (-6,1), as following:

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{1-3}{-6-(-7)}=-2[/tex]

- We know that the other line is connected with the point (-4,5), therefore, you can substitute values and solve for b:

[tex]5=-2(-4)+b\\5=8+b\\5-8=b\\b=-3[/tex]

Then, the equation for the line containing the side opposite the side containing the first two vertices is:

[tex]y=-2x-3[/tex]

Answer:

Step-by-step explanation:

If Lina supposedly bought 10 rolls, we would show it by the following equation,5*10=50, and since 25 is half of 50, we would have 5 as our solution.

25/5=5

5 rolls of films is our solution

Answer:

1320 ways

Step-by-step explanation:

Here we have a situation where 3 ribbons will be awarded to 3 of the 12 contestants. We can use the permutation formula, because the order of awarding the ribbons matters.

The permutation formula is:

[tex]_{n}P_{k}=\dfrac{n!}{(n-k)!}[/tex]

n = 12

k = 3

Now that we have our variables, let's plug them into the formula.

[tex]_{12}P_{3}=\dfrac{12!}{(12-3)!}[/tex]

[tex]_{12}P_{3}=\dfrac{12!}{9!}[/tex]

[tex]_{12}P_{3}=1320[/tex]

So there are 1320 different ways that the contestants will be awarded.

The answer is: There is no solution, it's not possible for Shawn to catch up with Jason since both are riding at the same constant speed, there is always be a distance of 1 mile between.

If it's possible to Shawn to catch up with Jason, the following equation will be true:

Let be the station our origin, so:

[tex]ShawnPosition=JasonPosition\\20mph.x-2miles=20mph.x-1mile\\-2=-1[/tex]

So, since the equation is not fulfilled, there is not solution, meaning that it's not possible to Shawn to catch up with Jason since both started riding from different points keeping the same constant speed, there will always be a distance of 1 mile between them if they keep the speed constant.

Also, Shawn could have caught up with Jason if he were started with a speed of 21mph instead the Jason speeds (20mph), let's prove that:

[tex]ShawnPosition=JasonPosition\\21mph.x-2miles=20mph.x-1mile\\\\21mph.x-20mph.x=2miles-1mile\\\\mph.x=1mile\\x=1h[/tex]

So, by substituting "x" into the equations, we have:

[tex]ShawnPosition=JasonPosition\\21mph.1h-2mile=20mph.1h-1mile\\21miles-2miles=20miles-1mile\\19miles=19miles[/tex]

So, Shawn could have caught up with Jason if he were started with a 21 mph speed  instead starting with the Jason speed (20 mph).

Have a nice day!

Answer:

[tex]x<8\frac{1}{4}[/tex]

Step-by-step explanation:

[tex]-4x+35>2\\-4x>-33\\x<\frac{33}{4} \\x<8\frac{1}{4}[/tex]

Remember to flip the sign when you divide or multiply both sides by a negative number! You don't need to flip the sign with adding or subtracting as in the case of step one subtracting 35 from both sides.

The solution of the inequality −4x+35>2 will be x < (33 / 4).

The relationship between two phrases using a symbol like "not equal to," "greater than," or "less than" indicates that they are not equal.

The given inequality will be solved as below:-

−4x+35>2

−4x>- 35 + 2

−4x > - 33

−4x > - 33

x < ( 33 / 4 )

Therefore, the solution of the inequality −4x+35>2 will be x < (33 / 4).

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Answer:

c

Step-by-step explanation:

The price of a plane ticket has increased by 33% from $150 to $200, determined by computing the difference between the new and old prices, dividing by the original price, and converting to a percentage.

The question is asking by what percent the price of a plane ticket has increased from $150 to $200. To calculate the percentage increase, you subtract the original price from the new price and divide by the original price. Then multiply by 100 to convert it to a percentage. Using this method:

So, the price of the plane ticket has increased by 33%, which means the correct answer is C) 33%.

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Answer:

Last choice that shows points on +4 and -4 is the correct graph.

Step-by-step explanation:

We have been given equation [tex]|m|=4[/tex]. Now we need to find out which of the given number lines shows the corret solution set for [tex]|m|=4[/tex].

We know that [tex]|x|=a[/tex] can be broken into two parts as:

[tex]x=+a[/tex] and [tex]x=-a[/tex]

Same way we can break [tex]|m|=4[/tex] into two parts as:

[tex]m=+4[/tex] and [tex]m=-4[/tex]

Hence last choice that shows points on +4 and -4 is the correct graph.

Answer:

D is correct

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

From the given coordinates

A(6, 0), B(0, 0) then AB = 6 - 0 = 6

B(0, 0), C(0, 8) then BC = 8 - 0 = 8

To calculate AC use Pythagoras' theorem on the right triangle formed

AC² = AB² + BC² = 6² + 8² = 36 + 64 = 100

Take the square root of both sides, hence

AC = [tex]\sqrt{100}[/tex] = 10

Perimeter = AB + BC + AC = 6 + 8 + 10 = 24 → C

Answer:

It should be $2.45.

Step-by-step explanation:

12.25 divided by 5 equals 2.45.

Answer:

1,350 students

Step-by-step explanation:

The number of students this year is 90% of the number from last year.  Find 90% of 1500....

90% is 0.9 as a decimal,

0.9(1500) = 1,350 students

Answer: 2i50 students

Step-by-step explanation:

Do 90% of 1,500

10% = 150

150 x 9 = 1350

We need the total amount of students

So do 1350 + 1500 = 2850 students

Answer:

1,2,4

Step-by-step explanation:

Factors are the numbers that we can multiply together to make 4

1*4 = 4

2*2 = 4

The factors are 1,2 and 4

Answer:

Step-by-step explanation:

[tex]Factors\ of\ 4:\ 1,\ 2,\ 4\\\\4=4\cdot\boxed{1}\\4=2\cdot\boxed2\\4=1\cdot\boxed4[/tex]

Answer:

The final solution is all the values that make  

( x 4  +  5  x 2  −  36 ) ( 2  x 2  +  9 x  −  5 )  =  0  true.  x  =  − 2 ,  2  ,  3  i  ,  −  3  i  , 1  2 ,  −  5

Step-by-step explanation:

x 4  +  5  x 2  −  36  =  0  2  x 2  +  9 x  −  5  =  0

Answer:

1,2,2,5,3

Step-by-step explanation:

it's right you idiots

Answer:

The Field's length is 93ft

Step-by-step explanation:

P=2L+2w

360=2(w+6)+2w

360=2w+12+2w

360=4w+12

348=4w

348/4=w

87=w

L=w+6

L=87+6

L=93

The width of a rectangular field surrounded by 360 feet of fencing is 87 feet. The length of the field, which is 6 feet more than the width, is 93 feet.

We are dealing with a rectangular field here, and we know that the length of a rectangle is equal to the total fencing (perimeter), divided by two, minus the width. Now, the problem states that the length is 6 feet more than the width. Therefore, we can create the following equation: 2x + 2(x + 6) = 360, where x is the width.

After simplifying this equation, we find that 4x + 12 = 360. Subtract 12 from both sides to get 4x = 348, and then divide by 4 to find that x = 87 feet. Thus, the width of the field is 87 feet. Since the length is 6 feet more than the width, we add 6 to 87 to get a length of 93 feet.

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Answer:

[tex]\frac{4}{36}[/tex] or [tex]\frac{1}{9}[/tex]

Step-by-step explanation:

We are given that Jack rolls two standard number cubes and we are to find the probability that the sum of the roll is 5, given that one cube up even and the other came up odd.

A sum of two from two rolls would always be one even and one odd, whatsoever is the case.

To have a sum of five, we can have (1, 4), (2,3), (3,2) or (4,1) out of a sample space of 36 so the probability will be [tex]\frac{4}{36}[/tex] or [tex]\frac{1}{9}[/tex].

The distance between rest stops on the new map is approximately 4.262 miles.

To find the distance between the rest stops on the new map, we need to determine the distance between each rest stop on the original map and then convert it to the new scale. The original map has a scale of 2 inches = 39 miles, so the distance between each rest stop on the original map is (9 inches / 7 rest stops) * 39 miles. Simplifying this gives us 5.571 miles. To convert this distance to the new scale, we use the scale of 1 inch = 30 miles. So, the distance between each rest stop on the new map is (5.571 miles / 39 miles) * 30 miles, which equals approximately 4.262 miles.

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The rest stops on the new map are approximately 19.2857 miles apart.

To find the distance between the rest stops on the new map, we need to determine the distance between the rest stops on the original map and then convert it to the new scale.

In the original map, the length of the highway is 9 inches and there are 7 rest stops.

Therefore, the distance between each rest stop on the original map is 9 inches / 7 rest stops = 1.2857 inches.

To convert this distance to the new scale, we multiply it by the ratio of the scales: 1.2857 inches * (1 inch / 2 inches) * (30 miles / 1 inch) = 19.2857 miles.

So, the rest stops on the new map are approximately 19.2857 miles apart.

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Answer:

Minimum area is : 1 * 35 = 35

Maximum area is : 19 * 17 = 323

Step-by-step explanation:

The parameter (P) of rectangle is calculated using:

P = 2(a+b)

We are given that,

P = 72

=> 2(a+b) = 72

=> a+b = 36

In rectangle, the lengths of both sides are different and a whole number (as mentioned in question), Therefore, the length of smaller side a can be varied from 1 to 17. Similarly, the length of larger side varies from 19 to 35.

The area can be easily calculated using a*b.

Minimum area is : 1 * 35 = 35

Maximum area is : 19 * 17 = 323

3 1/2 pints - 3/4 pints

3 1/2 = 3 2/4

3 2/4 = 2 6/4

2 6/4 - 3/4

2 3/4

Answer: 2 3/4 pints of berries

Sasha bought 3 and 1/2 pints of blueberries, ate 3/4 of a pint, and after calculating, she has 2 and 3/4 pints left for making jelly.

The student, Sasha, initially bought 3 and 1/2 pints of blueberries and then ate 3/4 of a pint. To find out how many pints of berries she has left, we need to subtract the amount eaten from the amount bought.

We calculate:

Converting 11/4 pints back to a mixed number, we get 2 and 3/4 pints. Therefore, Sasha has 2 and 3/4 pints of blueberries left to make jelly.

Answer:

The means is 8.5 The Median is 6

Step-by-step explanation:

1) to find the mean just Simply add all the numbers together and divided by how many numbers that is giving. (Because you are simply finding the average)

9+6+5+3+28+6+4+7=68

68 divided by 8 = 8.5

2) to find the median simply organize the numbers from least to greatest Like this: (3,4,5,6,6,7,9,28) Then keep crossing out from both sides teal you find the middle Number.

If there a odd amount of number the median will be one Number, if even 2 numbers ( if 2 numbers just add them both and divide by 2)

In This Case the Median is 6,6 but Its actually 6 Why (6+6=12) and (12/2=6) so your median is 6.

Hopes This helps!

The mean of the given data 9, 6, 5, 3, 28, 6, 4, 7 is 8.5 and the median is 6.

The mean is defined as the average of all the values or the mean can be defined as the sum of all observations by the total number of observations.

[tex]Mean =\dfrac {\ Sum \ of \ all \ observation}{Total \ number \ of \ observation}[/tex]

[tex]Mean = \dfrac{9 + 6 + 5 + 3 + 28 + 6 + 4 + 7}{8}[/tex]

Mean = [tex]\dfrac{68}{8}[/tex]

Mean  = 8.5

Therefore, the mean of the data set is 8.5.

The median is defined as:

The median is the middle value when the data set is arranged in ascending or descending order.

If there are two middle values, the median is the average of those two values.

Arrange the data set in ascending order: 3, 4, 5, 6, 6, 7, 9, 28.

Here n = 8, since n is even so the median is calculated as:

Median = [tex]\dfrac{(\dfrac{n}{2}) \ th \ observation + (\dfrac{n}{2}+1) \ th \ observation}{2}[/tex]

Median =[tex]\dfrac{( 4 \ th \ observation + 5 \ th \ observation)}{2}[/tex]

The 4th observation is 6 and the 5th observation is 6.

So, this mean will be 6.

Therefore, the median of the data set is 6.

The Mean is  8.5 and the median is  6.

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Answer:

$3116

Step-by-step explanation:

First off, we need to find the value of the appliance after the down payment.

$2450 - $600 = $1850

This then makes our principal $1850.

P = $1850

r = 9% or 0.09

t = 4 years

To find the total cost of the appliance plus interest, we need to look for our accrued amount first.

A = P + Prt

A = $1850 + $1850(0.09)(4)

A = $1850 + $666

A = $2516

Now that we know our accrued amount, we then add our down payment to find the total cost.

Total cost = $2516 + $600

Total cost = $3116

To calculate the cost of an appliance with added interest, subtract the down payment from the purchase price to determine the amount of the loan. This is followed by the calculation of the total interest over the length of the loan. Adding these two amounts provides the total cost of the appliance plus interest, which in this case is $2516.

The total cost of the appliance plus interest can be calculated by first determining the amount of the loan made, which is the cost of the appliance minus the down payment. This comes out to $2450 - $600 = $1850.

Then, the add-on interest over 4 years is calculated by multiplying the amount of the loan by the annual interest rate and by the number of years. For this question, that is $1850 * 0.09 * 4 = $666.

So, the total cost of the appliance with interest added is the sum of the amount of the loan and the amount of the interest. Therefore, $1850 + $666 = $2516 is the total cost for the appliance plus interest.

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Answer:

5

Step-by-step explanation:

3(2n-7)=9

^        ^

6n-21=9

   +21  +21

 6n=30

  6     6

n=5      :)

Answer:

Asa has $13 and owes $39

Step-by-step explanation:

25 + 14 = 39$ (amount of money he owes)

25 - 12 = 13$ (amount of money he has)