4. Find the slope of the line between the points (9,-12) and (5,4) ​

Answer:

1404.5 is your answer when you divide 8,427 by 6

Answer:

1404.5

Step-by-step explanation:

8427 divided by 6 in decimal = 1404.5

8427 divided by 6 in fraction = 8427/6

8427 divided by 6 in percentage = 140450%

Answer:

y = -2(x + 1)

Step-by-step explanation:

x-intercept of -1 means y=0 when x=-1, so you have your (x₁, y₁) value of (-1, 0).

Slope is -2 so m=-2.

Plug into point-slope formula:

y = m(x - x₁) + y₁

y = (-2)(x - (-1)) + (0)

y = -2(x + 1)

Answer:

Each golf ball costs about $2.

Step-by-step explanation:

Given:

Donald bought a box of golf balls for $9.27. There were 18 golf balls in the box.

Rename the decimal dividend as a whole number that is  compatible with the divisor to estimate the quotient.

Now, to find the cost of each golf ball.

As given:

Rename the decimal dividend as a whole number that is  compatible with the divisor to estimate the quotient.

As, the cost of golf ball box = $9.27.

So, 9.27 nearest to whole number is 9.

Thus to get the cost of each ball:

18 golf balls cost = $9.

So, 1 golf ball cost = [tex]18\div 9=2.[/tex]

Therefore, each golf ball costs about $2.                          

1 piece=3*12

=36

sp=36*35

=1260

profit=s.p-c.p

=1260-1008

=rs.252

Answer:

[tex]x=20.67\ ft[/tex]

Step-by-step explanation:

we know that

The Midpoint Theorem says that the line segment joining the midpoints of any two sides of a triangle is parallel to the third side and equal to half of the third side

so

in this problem

Applying the midpoint theorem

[tex]x=\frac{124}{3}:2=\frac{124}{6}=\frac{62}{3}=20.67\ ft[/tex]

Answer:

D) 34

Step-by-step explanation:

Since B is the midpoint, AB = BC

Plug the two in:

7x - 4 = 4x + 5

Solve for x:

3x = 9, x = 3

Find AB + BC

since BC = AB

AC = 4x + 5 + 4x + 5

AC = 8x + 10

AC = 8(3) + 10

AC = 24 + 10

AC = 34

The calculated length of the segment AC is () 34

From the question, we have the following parameters that can be used in our computation:

AB = 7x - 4

BC = 4x + 5

B is the midpoint of AC

So, we have

7x - 4 = 4x + 5

Evaluate

3x = 9

So, we have

x = 3

This means that

AC = 2 * (7 * 3 - 4)

Evaluate

AC = 34

HEnce, the length of the segment AC is () 34

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The area of shaded-region is 8.86 cm^2

Step-by-step explanation:

We can see that there is a circle and a triangle in the given figure

In order too find the area of shaded region, we have to find the area of rectangle and circle first. The area of the shaded region will be obtained by subtracting the area of circle from the area of rectangle.

So,

Area of circle:

Radius = r = 1 cm

So,

[tex]A_c = \pi r^2\\= 3.14 * (1)^2\\= 3.14*1\\= 3.14\ cm^2[/tex]

Area of rectangle:

Length of rectangle = l = 4 cm

Width of rectangle = w = 3 cm

So,

[tex]A_r = l*w\\= 4 *3\\=12 cm^2[/tex]

Now,

[tex]Area\ of\ shaded-region = A_r - A_c\\= 12 - 3.14\\=8.86\ cm^2[/tex]

The area of shaded-region is 8.86 cm^2

Keywords: Area, shaded regions

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Because she needs 3 blankets and it takes 15 day per blanket(rate is given), she needs 3x15 or 45 days. She has 60 days so she can volunteer at most 15 days.

answer: s≤15

Answer:

Option C) 27 people

Step-by-step explanation:

Let

x ----> the number of people

we know that

The cost of decorations ($35) plus the number of people (x) multiplied by the cost per person on food ($8.50) must be equal to $264.50

so

The linear equation that represent this situation is

[tex]35+8.50x=264.50[/tex]

solve for x

Subtract 35 both sides

[tex]8.50x=264.50-35[/tex]

[tex]8.50x=229.50[/tex]

Divide by 8.50 both sides

[tex]x=229.50/8.50[/tex]

[tex]x=27\ people[/tex]

Answer:

[tex]x=4\sqrt{2}\ units[/tex]

Step-by-step explanation:

Theorem: In the right triangle the leg is the geometric mean of the hypotenuse and the segment of the hypotenuse adjacent to the leg.

Based on the theorem above,

[tex]x^2=2\cdot (2+6)\\ \\x^2=4\cdot 8\\ \\x^2=32\\ \\x=\sqrt{32}\ units\\ \\x=4\sqrt{2}\ units[/tex]

Answer:

X=100

Step-by-step explanation:

X-(-300)=400

X+300=400

X=400-300

X=100

Answer:

x=100

Step-by-step explanation:

2 negatives make a positive

Answer:

x^2 + y^2 = 26.

Step-by-step explanation:

The center is at (0, 0) and the radius is sqrt (1^2 + 5^2) = sqrt 26

The general form is

x^2 + y^2 = r^2  so here it is:

x^2 + y^2 = 26.

Final answer:

The equation of the circle whose center is at the origin and passes through the point (1,5) is x² + y² = 25 since the radius of the circle is the distance from the origin to the point, calculated as 5.

Explanation:

If the point (1,5) lies on a circle whose center is at the origin, the equation of the circle can be found using the distance formula which is derived from the Pythagorean theorem. Since the distance from the center (0,0) to the point (1,5) is the radius of the circle, we calculate the radius as follows:

√((x-0)² + (y-0)²) = √((1-0)² + (5-0)²) = √(1 + 25) = √26 = 5.

Therefore, the radius of the circle is 5. The equation of the circle with a radius of 5, centered at the origin, is:

x² + y² = r²

x² + y² = 5²

x² + y² = 25

Answer:

Madhu's age= 21 and Sanku's age=7

Step-by-step explanation:

let the age of Madhu be x and age of Sanku be y.

now,

x=3y-equation (i)

then,

x-y=14

or,3y-y=14

or,2y=14

or,y=14/2

:. y=7

at last,putting value of y in equation(i)

x=3y

or,x=3x7

or,x=21

Therefore, Madhu's age is 21 and Sanku's age is 7

Answer:

$124.42

Step-by-step explanation:

look at the attachment for the formula I used

Answer:

y = -1/2x + 2

Step-by-step explanation:

A line in slope-intercept form in y = mx + b

"m" is the slope

"b" is the y-intercept

x and y represent points on the graph

To write an equation, you need "m" and "b".

We already know m = -1/2

The point (0, 2) is the y-intercept. The y-intercept occurs when x = 0.

Points are in the form (x , y), so x = 0 and y = 2.

Therefore b = 2.

Substitute m = -1/2 and b = 2 into the equation:

y = mx + b

y = -1/2x + 2

Answer:

2x+7y>=10

Replace x and y with 2 and 1

2*2+7*1>=10

2*2=4

7*1=7

4+7>=10

7+4=11

2x+7y>=10 is a true statement

Because 11 is greater than 10 and it doesnt have to be equal to 10 as long as its greater.

Answer:

No. it does not

Step-by-step explanation:

(i assumed you meant 2x+7y=10)

1.) 2(2)+7y=10

2.)2(2)+7(1)=10

3.)4+7=10

4.)11=10

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Multiply everything inside the brackets by -4

-4(3.2x) = -12.8x

-4(5y) = -20y

-4(-2.1) = 8.4

Put it together:

-12.8x - 20y + 8.4

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Answer:

2(7-2)=2(5)=10

Step-by-step explanation:

Answer: 14. 1 in

Step-by-step explanation:

The formula for calculating the length of an arc is given as :

L = Ф/360 x 2πr

where Ф is the angle subtended by the arc

r = radius

substituting the given values

L = 135/360 x 2 x 3.14 x 6

L = 5086.8/360

L = 14.13

L ≈ 14.1 in to the nearest tenth

Answer:

The answer is A

Step-by-step explanation:

edge 2021

E é usado para significar "10 à potência de". Por exemplo, 1.314E + 1 significa 1.314 * 101, que é 13.14.

Answer:

Step-by-step explanation:

2n + n    combine like terms

= 2n + 1n = (2 + 1)n = 3n

Answer:

3n

Step-by-step explanation:

2n + n Combine like terms

= 2n + 1n = (2+1)n= 3n

The 82nd term of the arithmetic sequence -8, 9, 26 can be solved using the arithmetic sequence formula, which results in the 82nd term being 1369.

The subject of this question is related to finding the 82nd term of the arithmetic sequence -8, 9, 26. Arithmetic sequences follow a pattern of adding a consistent value, this consistent value is called the common difference. From the given sequence, the common difference (d) can be calculated by subtracting the first term from the second term, or the second from the third, and so on. So d = 9 - (-8) = 17 or 26 - 9 = 17.

The formula for finding the nth term of an arithmetic sequence is a_n = a_1 + (n - 1) * d. Here, a_1 is the first term of the sequence and n is the term number we're interested in.

Thus, the 82nd term of the sequence can be found by substituting the values into the formula: a_82 = -8 + (82 - 1) * 17 = 1369. So, the 82nd term of the given arithmetic sequence is 1369.

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The [tex]82^{nd}[/tex] term of the arithmetic sequence -8, 9, 26, ..., is 1369.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is known as the common difference (d).

⇒ aₙ = a₁ + (n - 1) × d

where a₁ is the first term, n is the term number, and d is the common difference.

⇒ a₁ = -8.

⇒ d = 9 - (-8) = 17.

⇒ n = 82

⇒ a₈₂ = -8 + (82 - 1) × 17

⇒ a₈₂ = -8 + 81 × 17

⇒ a₈₂ = -8 + 1377

⇒ a₈₂ = 1369

Therefore, the [tex]82^{nd}[/tex] term of the sequence is 1369.

Complete question:

Find [tex]82^{nd}[/tex] term of the arithmetic sequence -8, 9, 26, ....

Final answer:

The variable x represents the unknown number, and the inequality is 4x - 6 < -2. Solving it step-by-step, we find that x < 1, which means any number less than 1 satisfies the inequality.

Explanation:

To solve the inequality 'four times a number decreased by 6 is less than -2', let's define a variable x as the number. Expressing the given condition as an inequality, we get 4x - 6 < -2. To solve for x, follow these steps:

Add 6 to both sides of the inequality to isolate the term with the variable: 4x - 6 + 6 < -2 + 6, which simplifies to 4x < 4.

Divide both sides of the inequality by 4 to solve for x: 4x/4 < 4/4, which gives us x < 1.

Check the answer to ensure it is reasonable. Since multiplying a number by four and subtracting six should result in a number less than -2, a number less than 1 seems reasonable.

Therefore, any number less than 1 satisfies the inequality.

Answer:

Number of rocks and fossils collected by you is 1 and  24 respectively

Number of rocks and fossils collected by your friend is 3 and 12 respectively

Step-by-step explanation:

Let  the number of Rocks you collect be x

Let  the number of Fossils you collect be y

Then the total number pf objects you collected will be

x + y = 25

x = 25 - y------------------------------(1)

Your friend collects three times as many rocks and half as many fossils as you.

This can be written as

[tex]3x + y(\frac{1}{2}) = 15[/tex]

[tex]3x + (\frac{y}{2}) = 15[/tex]-------------------(2)

Substituting (1) in (2)

[tex]3(25 -y) + (\frac{y}{2}) = 15[/tex]

[tex] 75 - 3y + (\frac{y}{2}) = 15[/tex]

Grouping the like terms we get,

[tex] 75 - 15 = 3y - (\frac{y}{2})[/tex]

[tex] 60= \frac{6y-y}{2})[/tex]

[tex] 60 \times 2= 6y-y[/tex]

[tex] 120= 5y[/tex]

[tex] y = \frac{120}{5}[/tex]

y= 24

Substituting  y value in equation(1) we get

x = 25 - 24

x= 1

Friends collects 3 times rock

so collects 3x =3(1) = 3rocks

Also he collects half as many fossils

That is

[tex]\frac{y}{2} = \frac{24}{2} =12 fossils[/tex]

You collect 1 rock and 24 fossils, while your friend collects 3 rocks and 12 fossils.

Let's assign variables to represent the number of rocks and fossils that you and your friend collect.

Let x represent the number of rocks you collect.

Since your friend collects three times as many rocks as you, we can represent the number of rocks your friend collects as 3x.

Let y represent the number of fossils you collect.

Since your friend collects half as many fossils as you, we can represent the number of fossils your friend collects as y/2.

From the information given, we know that you collect 25 objects, so we have the equation:

x + y = 25

We also know that your friend collects 15 objects, so we have the equation:

3x + y/2 = 15

Simplifying the second equation by multiplying both sides by 2, we get:

6x + y = 30

We now have a system of equations:

x + y = 25

6x + y = 30

Solving this system of equations, we can subtract the first equation from the second equation to eliminate y:

(6x + y) - (x + y) = 30 - 25

5x = 5

x = 1

Substituting the value of x into the first equation, we find:

1 + y = 25

y = 24

Therefore, you collect 1 rock and 24 fossils, while your friend collects 3 rocks and 12 fossils.

Yes they are linearly dependent, essentially the same equation.

Start from one of them:

-6 + y = 2x

Move things around:

y - 2x = 6

Multiply both sides by 2,

2y - 4x = 12

That's the second equation, which we've shown is equivalent to the first, so they're linearly dependent.

Answer:

14√3

Step-by-step explanation:

4√12 + 2√27

First, simplify both terms:

4√3√4 + 2√9√3

4 * 2√3 + 2 * 3√3

8√3 + 6√3

Now, combine the terms:

14√3

To find the sum of 4 radical 12 and 2 radical 27 in simplest form, we simplify each radical expression individually and then add the simplified expressions together, resulting in 5 times the square root of 3.

To find the sum of 4 radical 12 and 2 radical 27 in simplest form, we first need to simplify each radical expression individually. The square root of 12 can be simplified as the square root of 4 times the square root of 3, which is 2 times the square root of 3. Similarly, the square root of 27 can be simplified as 3 times the square root of 3.

Now, we can add these simplified radical expressions. 4 radical 12 plus 2 radical 27 equals (2 times the square root of 3) plus (3 times the square root of 3). This can be simplified as 5 times the square root of 3.

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Answer:

It can be represented by a ≥ 17.

Step-by-step explanation:

The rules concerning the age of a soccer player in a recreational league mandate that a player is 17 years of age or older.  

Therefore, if the age of a player is a years, then the condition for a soccer player to participate in the league is that a must be equal to 17 or more than 17 years old.

Hence, mathematically it can be represented by a ≥ 17. (Answer)

Solving for x...

4(x-3)=-8

Divide by 4.

x-3=-2

Add 3.

x=1

Answer: x = +1

Step-by-step explanation: To solve for x in this equation, our first step is to simplify the left side by distributing the 4 through both terms inside the parentheses.

When we do that, we get 4 times x which is 4x and 4 times -3 which is -12. So we have 4x - 12 = -8. Our next step is to isolate the x-term by adding 12 to both sides of the equation. On the left, -12 + 12 cancels and we are left with 4x. On the right, -8 + 12 simplifies to 4.

Now we have the equation 4x = 4.

To get x by itself, we divide both sides by 4 and x = +1.