The product of 9 and the sum of a number x and 4 is 6

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:

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:

-2w-20

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

given 1 pound = 16 ounces , then

5 pounds = 5 × 16 = 80 ounces

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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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.

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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Measures which examine the spread of different values around the measures of central tendency is measures of variability.

A central tendency in statistics is a typical or characteristic value for a probability distribution. Measures of central tendency are commonly referred to as averages in everyday speech. In the late 1920s, the phrase "central tendency" first appeared. The arithmetic mean, the median, and the mode are the three most popular ways to measure central tendency. The number used to represent the center or middle of a set of data values is known as the central tendency measure.

Given,

Measures which examine the spread of different values around the measures of central tendency:

B. Measures of variability

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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.    

(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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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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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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Answer:

480 lbs

Step-by-step explanation:

First, find the ratio of weight on the moon to weight on the earth. I will put the two known values in a fraction like this:

[tex]\frac{25}{150}[/tex]

Now, I can create a proportion, making sure to keep the same types of measurements in the numerator and denominator. I will use w for the unknown weight on earth.

[tex]\frac{25}{150}=\frac{80}{m}[/tex]

Now, I will simplify the fractions as much as I can.
[tex]\frac{1}{6}=\frac{80}{m}[/tex]

Now, I can see a correlation. 1 times 80 is 80, so 6 times 80 is m. Simplified, here is the answer!

[tex]6*80=m\\480=m\\m=480[/tex]

Answer:

480 pounds

Step-by-step explanation:

we times for objects on earth and divide for objects on the moon by the same number

150

[tex]150 \div x = 25[/tex]

150/-25=-x

-6/-1= -x/-1

6=x

[tex]150 \div 6 = 25[/tex]

so when in object is on earth you multiple by x Wich 6

[tex]80 \times 6 = 480[/tex]

you can also cross multiply

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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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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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.

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!!

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:

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

Answer: 163$

Step-by-step explanation:

The number that will be next in the series will  be  63 .

In the question ,

a recurrence relation is given that is  0, 3, 8, 15, 24, 35, 48, ? .

we have to find the number that will come in place of question mark .

On carefully examining the series , we can see that

3 - 0 = 3

8 - 3 = 5

15 - 8 = 7

24 - 15 = 9

35 - 24 = 11

48 - 35 = 13

we can se that increments 3,5,7,9,11,13,... form an Arithmetic Progression

with first term as 3 and common difference as 2 ,

So ,the next increment will be 13+2 = 15

let the next term be "x" .

x - 48 = 15

x = 15 + 48 = 63

the number in place of ? is 63 .

Therefore , The number that will be next in the series will  be  63 .

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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.

You got to set it up to boys to girls

Answer:

0,1

Step-by-step explanation:

simplest form

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]

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

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:

A ≈ 6538.35 cm²

Step-by-step explanation:

Calculating the area (A) using Heron's formula

A = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]

where s is the semi perimeter and a, b, c the 3 sides

here

s = 380 ÷ 2 = 190

given perimeter = 380 and unequal side is 150 , then

equal sides = (380 - 150) ÷ 2 = 230 ÷ 2 = 115 cm

then a = 150, b = 115 , c = 115

A = [tex]\sqrt{190(190-150)(190-115)(190-115)}[/tex]

   = [tex]\sqrt{190(40)(75)(75)}[/tex]

   = [tex]\sqrt{42750000}[/tex]

   ≈ 6538.35 cm² ( to 2 dec. places )

The distance on the map, in cm, given the real distances, and the scale of the map are:

A scale of 1 : 200, 000 means that every 1 cm on the map is 200, 000 cm on the ground.

To find the distance on the map of 10 km, first convert it to cm:
= 10 km x 100, 000 cm per km

= 1, 000, 000 cm

The distance on the map is therefore:

= 1, 000, 000 / 200, 000 cm scale

= 5 cm on map

The distance of 15 km on the map is:

= (15 km x 100, 000) / 200, 000

= 7.5 cm

The distance of 4 km is:

= (4 x 100, 000) / 200, 000

= 2 cm

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The total number of toys is 45 Samuel if Samuel has a collection of toy cars. His favorites are the 27 red ones.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

It is given that:

Samuel has a collection of toy cars. His favorites are the 27 red ones.

Let Samuel has x number of toys:

From the equation:

60% of x = 27

(60/100)x = 27

0.6x = 27

x = 27/0.6

x = 45

Thus, the total number of toys is 45 Samuel if Samuel has a collection of toy cars. His favorites are the 27 red ones.

The complete question is:

Samuel has a collection of toy cars. His favorites are the 27 red ones which make up 60% of his collection. How many toy cars does Samuel have?

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Answer:156

Step-by-step explanation:

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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