Which ordered pair is a solution of the linear equation system
x + 4y = 18 and -3x + 2y = 16?

F. ( -2,-5)
G. (-2, 5)
H. (2, 5)
I. (2, -5)

Answer:

=============================

The given translates as:

Use given x - intercepts to get the equation:

Use the coordinates of P to find the value of a:

The equation of this parabola is:

Answer:

[tex]\textsf{Intercept form}: \quad y=-\dfrac{2}{7}(x+4)(x-7)[/tex]

[tex]\textsf{Standard form}: \quad y=-\dfrac{2}{7}x^2+\dfrac{6}{7}x+8[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6 cm}\underline{Intercept form of a quadratic equation}\\\\$y=a(x-p)(x-q)$\\\\where:\\ \phantom{ww}$\bullet$ $p$ and $q$ are the $x$-intercepts. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]

If the x-intercepts are (-4, 0) and (7, 0) then:

Substitute the values of p and q into the formula:

[tex]\implies y=a(x-(-4))(x-7)[/tex]

[tex]\implies y=a(x+4)(x-7)[/tex]

To find a, substitute the given point on the curve P (3, 8) into the equation:

[tex]\implies 8=a(3+4)(3-7)[/tex]

[tex]\implies 8=a(7)(-4)[/tex]

[tex]\implies 8=-28x[/tex]

[tex]\implies a=\dfrac{8}{-28}[/tex]

[tex]\implies a=-\dfrac{2}{7}[/tex]

Substitute the found value of a into the equation:

[tex]\implies y=-\dfrac{2}{7}(x+4)(x-7)[/tex]

Expand to write the equation in standard form:

[tex]\implies y=-\dfrac{2}{7}(x^2-3x-28)[/tex]

[tex]\implies y=-\dfrac{2}{7}x^2+\dfrac{6}{7}x+8[/tex]

Answer:

12x^5+18x^2+10x^3+15

Step-by-step explanation:

first you apply the distribution property (FOIL) and you get

12x^5+18x^2+10x^3+15

Answer:

Step-by-step explanation:

y=7x is the equation that shows how the total cost of the party favors, y, depends on the number of guests, x

Two or more expressions with an Equal sign is called as Equation.

Given,

Andrew has picked out some party favors.

He calculates that they will cost $7 per guest.

We need to find the equation that shows how the total cost of the party favors, y, depends on the number of guests, x

So y=7x where y is the total cost and x is the number of guests and 7 is the cost per guest.

If there are 2 guests then the total cost will be 14.

Hence y=7x is the equation that shows how the total cost of the party favors, y, depends on the number of guests, x

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The net value of the items purchased is ₹ 900.

Raman purchased books and stationery items and paid the total amount of rupees 963.

Paid tax = 7%

Let the net value of the items purchased be `x.

VAT = 7%

Selling price = ₹x + (7% of x)

                    = ₹x+ ₹ ( 7/100 * x)  

                    =₹( x +7 x /100)

                    = ₹ 107 x /100

But Raman purchased books and stationery items for ₹963.

107x/100 = ₹963

               x =  963 x 100/107

               x = 900

Hence the answer is the net value of the items purchased is ₹ 900.

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By solving a system of equations we can see that each goat costs $30 and each sheep costs $25.

Let's define the variables:

x = cost of a goat

y = cost of a sheep.

We can write the system of equations with the given info:

6*x + 5*y = 305

2*x + 9*y = 285

If we subtract 3 times the second equation from the first one, we get:

(6*x + 5*y) - 3*(2*x + 9*y) = 305 - 3*285

-22*y = -550

y = -550/-22 = 25

Now that we know the value of y we can try to find the value of x:

2*x +9*25 = 285

2*x = 285 - 9*25 = 60

x = 60/2 = 30

These are the costs of each animal.

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Answer:

Step-by-step explanation:

The average annual rainfall for a town is 43.2 inches.

This is converted to average monthly as:

The difference is:

Answer:

Yeah, they exceeded by 0.4 inches.

Step-by-step explanation:

It is given that,

→ the average monthly rainfall for the previous 9 months was 4 inches.

The monthly rainfall in 12 months,

→ 43.2 inches ÷ 12 months

→ 43.2/12

→ 3.6 inches

Then the difference will be,

→ 4 inches - 3.6 inches

→ 4 - 3.6

→ 0.4 inches

Hence, the difference is 0.4 inches.

The linear equation two variables can be solved by various methods one of the methods to solve the linear equations is the substitution method. The solution of the given equation is x=2 and y=10.

What is  linear equation in two variables ?

A specific point on the graph represents the solution of a linear equation in two variables, ax+by = c, where the total of these two values will equal c when the x-coordinate is multiplied by a and the y-coordinate by b.

Main body:

The given equations are :

10x+3y=50     .... (1)

-5x-y=-20      ....(2)

Multiply equation (2) by 3 and then add the equation (1) to eliminate the variable y.

10x+3y+3(-5x-y)=50+3*-20

-5x=-10

x=2

Now putting the value of x in equation (1), and solve it further.

10*2+3y=50

3y=30

y=10

Hence, the value of x is 2 and the value of y is 10.

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Answer:

Arithmetic

Step-by-step explanation:

The difference between consecutive terms is 5. Thus, this is an arithmetic sequence with a common difference of 5.

a. Creating a system of equations, the length of each plan A's workout is 3/4 hour, while the length of each plan B's workout is 3/4 hour.

b. x = -8, y = 2.

Write equations of a system that represents the information given and solve accordingly.

Let the length of plan A = x

Length of plan B = y

Equation for Monday would be:

9x + 7y = 12 --> eqn. 1

Equation for Tuesday:

3x + 5y = 6 --> eqn. 2

Multiply eqn. 1 by 3 and eqn. 2 by 9

27x + 21y = 36 --> eqn. 3

27x + 45y = 54 --> eqn. 4

Subtract the equations:

-24y = -18

y = -18/-24

y = 3/4

Plan B's length of workout is: 3/4 hour.

Substitute y = 3/4 into equation 2:

3x + 5(3/4) = 6

3x + 15/4 = 6

3x = 6 - 15/4

3x = 9/4

12x = 9

x = 9/12

x = 3/4

Length of plan A's workout is: 3/4 hour.

b. 2x + 4y = -8 --> eqn. 1

-2x + 3y = 22 --> eqn. 2

Add both equations together:

7y = 14

y = 2

Substitute y = 2 into equation 1:

2x + 4(2) = -8

2x + 8 = -8

2x = -8 - 8

2x = -16

x = -16/2

x = -8

The solution is: x = -8, y = 2.

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========================================================

Explanation:

A thing that jumps out at me right away is the presence of x/3 on both sides. When subtracting x/3 from both sides, these terms cancel out and we're left with this equation

5 = 6 + (x/9)

Let's say w = x/9. We now have this equation 5 = 6 + w. Subtract 6 from both sides to isolate w and you should get w = -1

Then plug in w = x/9 and solve for x.

w = -1

x/9 = -1

x = 9*(-1)

x = -9

We get exactly one solution and it is x = -9

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

Check:

5 + x/3 = x/3 + 6 + x/9

5 + (-9)/3 = (-9)/3 + 6 + (-9)/9

5 - 3 = -3 + 6 - 1

2 = 3 - 1

2 = 2

We get the same thing on both sides, which leads to a true statement. This causes a domino effect to lead the first equation to be true when x = -9. Therefore, the solution is confirmed.

Answer: 2>=n

Step-by-step explanation:

3n-6 +2 >= 5n-8

3n-4 >= 5n-8

-4>= 2n -8

4>=2

2>=n

Hope this helped!!

The measure of angle 2 is 75°

From the question, we have

∠1= 105°

∠2= 180°- 105° (Linear pair)

∠2=75°

Subtraction:

Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.

The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.

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23 tickets are purchased for children and 9 tickets are purchased for adults.

Given,

In the question:

A group entering a zoo purchased 32 admission tickets for a total of $148. Adult tickets cost $7. 50, and tickets for children cost $3. 50.

To find the how many of each type of ticket were purchased?

Now, According to the question:

It is given in the question that 32 tickets are purchased by group which cost total $148.

Let the number of children of the group who are entering the zoo be x. Then the number of adults will be 32- x

Now cost of one ticket for adult = $7.50

Total amount spent on adult tickets = 7.50 × (32-x)

Similarly, cost of one ticket for child= $3.50

Total amount spent on children tickets = 3.50 × x =3.5x

Total amount spent by group on tickets =  $148

⇒ 7.5 × (32-x) + 3.5x = 148

⇒ 240 - 7.5x + 3.5x = 148

⇒ 7.5x - 3.5x = 240 - 148

⇒ 4x = 92

⇒ x = 23

Children = 23

Adults = 32-x = 32-23 = 9

Hence, 23 tickets are purchased for children and 9 tickets are purchased for adults.

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Answer:

which of the following ratios are connected to 5/20?

multiple choice

a 1/5

c 20/100

d 25/100

d is the option 25/100 and

b 1/4

If there are 80 cow and 30 buffaloe , the ratio of the cow and the buffaloe is 8:3  .

In the question,

it is given that ,

the number of cows in the farm house = 80

the number of buffaloe in the farm house = 30

we need to find the ratio of cow and the buffaloe .

the ratio can be calculated using the formula .

ratio = (number of cows)/(number of buffaloe)

Substituting the vales , we get

= 80/30

cancelling out the common factor 10 , from both numerator and denominator , we get

= 8/3

So , the ratio is 8:3   .

Therefore ,  If there are 80 cow and 30 buffaloe , the ratio of the cow and the buffaloe is 8:3  .

The given question is incomplete , the complete question is

In a farm house, there are 80 cows and 30 buffaloes . What is the ratio of the cow and the buffaloe ?

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Answer:

33.  AB = √45.  CD = √40.  Not congruent.  AB is greater.

34.  EF = 5.  GH = √41.  Not congruent.  GH is greater.

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]

Given endpoints:

Substitute the given endpoints into the formula and solve:

[tex]\begin{aligned}\overline{AB}&=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\&=\sqrt{(-3-0)^2+(8-2)^2}\\&=\sqrt{(-3)^2+(6)^2}\\&=\sqrt{9+36}\\&=\sqrt{45}\\& \approx 6.7\; \sf (1 \; d.p.)\end{aligned}[/tex]

Given endpoints:

Substitute the given endpoints into the formula and solve:

[tex]\begin{aligned}\overline{CD}&=\sqrt{(x_D-x_C)^2+(y_D-y_C)^2}\\&=\sqrt{(0-(-2))^2+(-4-2)^2}\\&=\sqrt{(2)^2+(-6)^2}\\&=\sqrt{4+36}\\&=\sqrt{40}\\& \approx 6.3\; \sf (1 \; d.p.)\end{aligned}[/tex]

Therefore, the segments at not congruent.

[tex]\textsf{As\; $\sqrt{45} > \sqrt{40}$ \; then \; $\overline{AB} > \overline{CD}$}.[/tex]

Therefore, the length of segment AB is greater.

Given endpoints:

Substitute the given endpoints into the formula and solve:

[tex]\begin{aligned}\overline{EF}&=\sqrt{(x_F-x_E)^2+(y_F-y_E)^2}\\&=\sqrt{(5-1)^2+(1-4)^2}\\&=\sqrt{(4)^2+(-3)^2}\\&=\sqrt{16+9}\\&=\sqrt{25}\\&=5\end{aligned}[/tex]

Given endpoints:

Substitute the given endpoints into the formula and solve:

[tex]\begin{aligned}\overline{GH}&=\sqrt{(x_H-x_G)^2+(y_H-y_G)^2}\\&=\sqrt{(1-(-3))^2+(6-1)^2}\\&=\sqrt{(4)^2+(5)^2}\\&=\sqrt{16+25}\\&=\sqrt{41}\\& \approx 6.4\; \sf (1 \; d.p.)\end{aligned}[/tex]

Therefore, the segments at not congruent.

[tex]\textsf{As\; $\sqrt{41} > 5$ \; then \; $\overline{GH} > \overline{EF}$}.[/tex]

Therefore, the length of segment GH is greater.

Answer:

Step-by-step explanation:

We have to the graph from x = -4 to x = 2

2y + x + 3 = 0

Rearrange the equation to make y the subject

2y = -x - 3

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

-3/2 is the y intercept

the gradients is -1/2

since the value is negative, the graph will be sloping downwards

Point your pen at y = -3/2 on the y axis (-3/2 is -1.5)

go 1 point down and 2 points to the right, make a point and connect these 2 dots and make a line across the graph.

Do the same with the other equation:

3y - x + 1 = 0

3y = x - 1

y = (1/3)x -1/3

y intercept is -1/3

gradient is 1/3

point your pen at -1/3 on the y axis, go 1 point up and 3 points to the right

and mark this point and connect these 2 points and make a line across the graph.    

Answer:

-2w-20

Step-by-step explanation:

The rule that describes ( -1, 1), (1, 2), (3, 3), (5, 4) is c. Output = (0.5)(Input) + 1.5

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, On a coordinate plane, points are at ( -1, 1), (1, 2), (3, 3), (5, 4).

By observing the given options we conclude that it is Output = (0.5)(Input) + 1.5 to confirm let's put the values.

Given when input is - 1 output is 1.

∴ 1 = 0.5(-1) + 1.5.

1 = - 0.5 + 1.5.

1 = 1  ( satisfied).

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Plotting the graph of the quadratic function  g(x)=-1/5x^2 + 4x + 1 the range is

The range of the quadratic function is seen at the vertex were the maximum or minimum y value is seen

The graph of the function  g(x)=-1/5x^2 + 4x + 1 is plotted and attached

From the graph the vertex coordinates is v(-10, -16). The y coordinates of the vertex is -19 and this is the minimum values for y

Therefore the range is y ≥ -19

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Answer:

B

Step-by-step explanation:

given 1 pound = 16 ounces , then

5 pounds = 5 × 16 = 80 ounces

The length of the line YZ is 26 units

The Y is the mid point of the line XZ

The length of the line XY = 20 + 2a

The length of the line YZ = 8 + 6a

When Y is the mid point of the line XZ, then the length of the line XY is equal to the length of the line YZ

The length of the line XY = The length of the line YZ

Substitute the values in the equation and find the value of a

20 + 2a =  8 +6a

Rearrange and group the like term

6a - 2a = 20 - 8

4a = 12

a = 12 / 4

a = 3

The length of the YZ = 8 +6a

= 8 + 6×3

= 8 + 18

= 26 units

Hence, the length of the line YZ is 26 units

The complete question is:

Find the length of YZ when Y is the midpoint of XZ, if XY = 20+2a and YZ = 8+6a.

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Answer:

2.8 pounds per hour

Step-by-step explanation:

[tex] \frac{3.5}{1.25} = \frac{350}{125} = \frac{14}{5} = 2.8[/tex]

The function f has domain : [-4, 5], range : [0, 9], zero : (3, 0), the function is increasing in intervals at [-4, 0] U [3, 5], decreasing in intervals at (0, 3], the relative minimum values of f : (3, 0), and relative maximum values of f : (5, 9).

The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.

The function f is given in the graph.

According to the given function, the required solution would be as:

The domain and range of f will be :

domain : [-4, 5]

range : [0, 9]

The zero of f will be :

(x, y) = (3, 0)

The function is increasing in intervals at [-4, 0] U [3, 5]

The function is decreasing in intervals at (0, 3]

The relative minimum values of f : (3, 0)

The relative maximum values of f : (5, 9)

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(a)The probability that the friend is between 25 and 30 minutes late is 1/2.

(b) It is 10 A.M. There is a 10% probability the friend will arrive within 1 minute.

What is probability?

Uniform distribution

a = 0

b = 10

a) P(friend is between 25 and 30 minutes late) = (30 - 25)/(b - a)

= 5/(10-0)

= 1/2

b) Let the time for arrival be A minutes

(A - 0)/(b-a) = 0.10

A = 0.10 x (10 - 0)

A = 1 minute

Hence, The probability that the friend is between 25 and 30 minutes late is 1/2 and It is 10 A.M. There is a 10% probability the friend will arrive within 1 minute.

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Answer:

4/7

Step-by-step explanation:

2/7 ÷ 1/2 = 2/7 × 2/1 = 4/7

Answer:

Step-by-step explanation:

1. Write Words into math

2/7/1/2

2. Solve

2/7/1/2=

2/7*2/1=

4/7

Answer: 4/7

1) the speed of Simon per hour is 128 miles/Hr

2) The length of IG is 20 Units.

3) The ratio of SM is 2:1

1) For 1, to obtain the speed of Simon per hour, all you need to do is multiply 32 x 4.
This is because in every hour, 15 minutes occurs four times. That is:

1 hour = 60 minutes

Hence, if 32 miles is done in 15 minutes, then 60 minutes =

32 x 4

= 128 miles

Hence the speed of Simon per hour is 128 Miles/ Hour

2) Given that the two triangles are identical, it means that on the basis on RHS  theorem we have been given all the sides. Note that BG is 6 Units (we are assuming that this is the base) , then AT from the other triangle (see attached) is 20.

We assume this is the Hypotenuse. CT is also given. We assume this is the height. If we have CT and AT, and both triangles are the same, then IG is 20 units.

3) For the quadrilateral, recall that in quadrilaterals opposite sides are equal. If one side is 34u on one, and the other side is 17u on the other quadrilateral, then we already have the measure of the sides for both quadrilaterals.

So the Ratio of AK to WN

34u: 17u - Simplified by dividing by 17u we have

Ratio 2:1

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Answer:156

Step-by-step explanation:

If the actual length of the pool table is 6 feet , then the length of the pool table in the drawing is 12 inches   .

In the question,

it is given that ,
Barbara drew an scale drawing of the game room.

the scale that she used is 1 feet in the actual length is represented by 2 inches in the drawing ,

which means ,

1 feet = 2 inches

to find the length of 6 feet in the drawing ,

6 feet = 6 × 2 inches

= 12 inches

Therefore , If the actual length of the pool table is 6 feet , then the length of the pool table in the drawing is 12 inches   .

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