Solve |12x + 1| = 10
(9/2, 11/2)
(-9/2, 9/2)
(-112.9/2)

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:

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.

The value of x is 4.

Step-by-step explanation:

Consider a Rectangle ABCD

AB as Top

CD as Bottom

AB = -1 + 4x

CD = 3x + 3

To Find:

x = ?

Solution:

In a Rectangle ABCD

Opposite sides of rectangle congruent,

AB = CD

Top = Bottom

on substituting we get

[tex]-1+4x=3x+3\\\\4x-3x=3+1\\\\x=4\\\therefore x =4[/tex]

The value of x is 4.

Answer:

$124.42

Step-by-step explanation:

look at the attachment for the formula I used

Answer:

Choosing a 6 and then a prime number: 2/21

Choosing two odd numbers: 2/7

Step-by-step explanation:

Choosing a 6 and then a prime number:

The probability of choosing 6 out of 1, 2, 3, 4, 5, 6 and 7 is one event divided by number of total events (which is equal to 7). That results in 1/7. Once 6 is chosen, the probability of choosing a prime number (prime number is a number that can only be divided by 1 and itself) out of 1, 2, 3, 4, 5 and 7 is 4/6 (prime numbers are 2, 3, 5, 7 in total there are 4 number and total number of events are 6). Finally, the probability of choosing a 6 and then a prime number is (1/7)*(4/6)=2/21.

Choosing two odd numbers:

The probability of choosing 1st odd number is 4/7 (number of odd numbers is 4 which includes 1, 3, 5, 7 and the number of total events is 7). Once 1st odd number is chosen, the probability of choosing 2nd odd number is 3/6 (number of odd numbers is 3 - because 1 odd number is already chosen and the number of total events is 6). Finally, the probability of choosing two odd numbers in a sequence is (4/7)*(3/6)=2/7.

Answer:

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

Step-by-step explanation:

1 piece=3*12

=36

sp=36*35

=1260

profit=s.p-c.p

=1260-1008

=rs.252

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:

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:

[tex]2\sqrt{2}\ units[/tex]

Step-by-step explanation:

we know that

In a 45-45-90 right triangle, the length of the two legs are equal

so

Applying the Pythagorean Theorem

[tex]c^2=a^2+b^2[/tex]

where

c is the hypotenuse

a and b are the legs

we have

[tex]a=2\ units\\b=2\ units[/tex]

substitute

[tex]c^2=2^2+2^2[/tex]

[tex]c^2=4+4[/tex]

[tex]c^2=8[/tex]

[tex]c=\sqrt{8}\ units[/tex]

simplify

[tex]c=2\sqrt{2}\ units[/tex]

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:

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)

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:

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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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]

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, ....

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:

lol

Step-by-step explanation:

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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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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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:

Slant height (s)= 12.1 cm

Step-by-step explanation:

Given: Base= 4.5 cm.

           Surface area of right square pyramid= 129.5 cm.

First, calculating slant height (s) of right square pyramid.

Surface area of square pyramid= [tex](a^{2} +2\times a\times s)[/tex]

a= side of square base.

s= slant height

∴ [tex]129.5= (4.5^{2} + 2\times 4.5\times s)[/tex]

⇒ [tex]129.5= (20.25+2\times 4.5\times s)[/tex]

⇒ [tex]129.5= (20.25+9\times s)[/tex]

Now, opening the parenthesis and subtracting both side by 20.25.

⇒ [tex]109.25=9\times s[/tex]

cross multiplying both side

∴ Slant height (s)= 12.1

Final answer:

To find the slant height of the right square pyramid, subtract the base area from the total surface area, divide by four to find the area of one triangular side, and then solve for the slant height using the triangle area formula. The calculated slant height is = 12.1 cm

Explanation:

The student is asking how to find the slant height of a right square pyramid when given the surface area and the base length. To solve this, we need to take into account the formula for the total surface area of a right square pyramid, which is the sum of the base area and the area of the four triangles forming the sides. We know the total surface area is 129.5 cm2 and the base length is 4.5 cm. The area of the base is simply the square of the base length since it's a square base.

Base area = base length2 = (4.5 cm)2 = 20.25 cm2

Total area of four triangular sides = 129.5 cm2 (total surface area) - 20.25 cm2 (base area) = 109.25 cm2

Area of one triangular side = 109.25 cm2 / 4 = 27.3125 cm2

Now, using the formula for the area of a triangle, A = 1/2 × base × height, we can substitute the area of one triangular side and the base length to solve for the slant height:

27.3125 cm2 = 1/2 × 4.5 cm × slant height (s)

Slant height (s) = (2 × 27.3125 cm2) / 4.5 cm = 12.139 cm

Rounded slant height = 12.1 cm

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

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.

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:

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: 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

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

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