What are the solutions to the equation (2x - 5)(3x – 1) = 0?
O x=-zor x=
O x=] or x=3
0
0
O
x = 5 or x = 1

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]

The constant of variation here is the reading speed, which is 14 pages per hour.

The student reads 56 pages in 4 hours. To find out how many pages the student will read in 7 hours, we first calculate the constant of variation, which is the student's reading speed per hour. We divide 56 pages by 4 hours to get a reading speed of 14 pages per hour. To find the total number of pages read in 7 hours, we multiply the hourly reading speed by 7 hours.

Calculate hourly reading speed: 56 pages   4 hours = 14 pages/hour.

Multiply the hourly reading speed by the number of hours: 14 pages/hour   7 hours.

The student is expected to read 98 pages in 7 hours (14 pages/hour   7 hours = 98 pages).

hence, the student's constant of variation is their reading speed, which is 14 pages per hour. By multiplying this constant by 7 hours, we find that the student will read 98 pages in 7 hours.

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

1 piece=3*12

=36

sp=36*35

=1260

profit=s.p-c.p

=1260-1008

=rs.252

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.

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

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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.

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:

$124.42

Step-by-step explanation:

look at the attachment for the formula I used

Answer:

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

Step-by-step explanation:

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.                          

Answer:

y = 0

Step-by-step explanation:

1 c.

If we have an exponential function of the form  [tex]f(x)=a^x[/tex], where "a" is any positive integer, say, then that function will take the general shape of the function shown in the picture.

It will always approach the x-axis but never meet (touch). Any line that a function (graph) approaches but never touches, is known as an asymptote to the graph.

Since the function  [tex]f(x)=4^x[/tex]  follows the path of the general form shown above, this also approaches the x-axis, but never touches. So, the x-axis is the asymptote of the function.

We know

x-axis has equation  y = 0, and

y-axis has equation x = 0

Here, the x-axis is the asymptote, so the equation is:

y = 0

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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:

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:

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:

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=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:

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

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

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

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:

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:

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:

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)

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

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

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.