Four more than seven times a number is the same as twenty less than three times the number. Find the number

Here is the equation:

43.25 = 1.25t + 7 where t is the number of minutes he was on the trampoline.

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Work Shown:

C = 44 is the circumference

in general, the circumference of a circle is

C = 2*pi*r

Plug in C = 44 and solve for r.

C = 2*pi*r

44 = 2*pi*r

2*pi*r = 44

r = 44/(2pi)

r = 7.0028175 which is approximate

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Now plug this into the formula for the area of a circle

A = pi*r^2

A = pi*(7.0028175)^2

A = 154.061985

A = 154 rounding to the nearest whole number

Answer:

B

Step-by-step explanation:

Circumference = 2πr

And circumference = 44 m

44 = 2πr

so, r = 44/2π

r = 22/π

Radius is 22/π

Area of circle = πr²

Area of circle = π × (22/π)²

Area of circle = π × 22²/π²

Area of circle = 22²/π

Area of circle = 484/π

Area of circle = 154.14m²

Answer:

option (2)

Step-by-step explanation:

Given the area (A) of a circle is

A = πr² ← r is the radius ( divide both sides by π )

[tex]\frac{A}{\pi }[/tex] = r² ( take the square root of both sides )

[tex]\sqrt{\frac{A}{\pi } }[/tex] = r → option (2)

Answer:

7. [tex]\frac{1}{2}+\frac{1}{3}>\frac{1}{5}[/tex]

8. [tex]0.1+0.15>0.2[/tex]

Step-by-step explanation:

Given:

Three sides of the triangles are given.

For Question 7

1/2 _ 1/3 _1/5

For Question 8

0.1 _ 0.15 _ 0.2

We need to use >, <, and + signs to write inequalities for the relationships among  the sides of the triangles.

Solution:

Part 7.

Property of the triangles.

Sum of two side of triangles must be greater than third side.

So, first, second and third side of the triangle is [tex]\frac{1}{2}, \frac{1}{3}\ and\ \frac{1}{5}[/tex]

[tex]\frac{1}{2}+\frac{1}{3}>\frac{1}{5}[/tex]

[tex]\frac{5}{6}>\frac{1}{5}[/tex]

So, its satisfy the triangle rule.

Therefore, Inequality is [tex]\frac{1}{2}+\frac{1}{3}>\frac{1}{5}[/tex]

Part 8.

Property of the triangles.

Sum of two side of triangles must be greater than third side.

So, first, second and third side of the triangle is [tex]0.1, 0.15\ and\ 0.2[/tex]

[tex]0.1+0.15>0.2[/tex]

[tex]0.25>0.2[/tex]

So, its satisfy the triangle rule.

Therefore, Inequality is [tex]0.1+0.15>0.2[/tex]

Use inequalities to compare sides of triangles with >, <, and + signs.

For 7:

1/2 > 1/3

1/3 > 1/5

1/2 + 1/3 > 1/3 + 1/5

For 8:

0.1 < 0.15

0.15 < 0.2

0.1 + 0.15 < 0.15 + 0.2

Answer:

B) 3(2x+3)^2

Step-by-step explanation:

12x^2+36x+27

factor out the 3 first,

3(4x^2+12x+9)

factor out the trinomial 4x^2+12x+9,

3(2x+3)(2x+3)

3(2x+3)^2

Answer:

B. 3(2x + 3)2

Step-by-step explanation:

See explanation

Step-by-step explanation:

A situation where a farmer needs to divide his 5 acre land into 1/2 an acre to get 10 pieces of land where he can grow ten different crops.

In such a case; you divide 5 by 1/2

5/ 1/2 = 5*2 =10 pieces

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Answer:can someone help

Step-by-step explanation:

Answer:

[tex]\large \boxed{\text{39 ft}}[/tex]

Step-by-step explanation:

Let x be the distance from the foot of the ladder to the base of the building.

We have a right triangle, so we can use Pythagoras' Theorem.

[tex]\begin{array}{rcl}80^{2} + x^{2}& = & 89^{2} \\6400+ x^{2} & = & 7921\\x^{2} & = & 1521\\x & = & \sqrt{1521}\\& = &\mathbf{39}\\\end{array}\\\text{The foot of the ladder will be $\large \boxed{\textbf{39 ft}}$ from the base of the building,}[/tex]

Answer:

f^-1 (x)=1/5x-4/5

Step-by-step explanation:

y=5x+4

x=5y+4

5y=x-4

y=1/5x-4/5

Answer:

I WOULD SAY THAT THE ANSWER IS C

Step-by-step explanation:

I GOT IT FROM A

                          P

                          E

                          X

Answer:

y = 5/2 , x= 7/2

Step-by-step explanation:

5x - 3y = 10…....(1)

3x + 3y = 3......(2)

solving by elimination, we subtract equation (2) from equation (1)

so, 2x = 7

dividing both sides by 2

x= 7/2

substitute x=7/2 for the value of y in equation (1)

5(7/2) - 3y = 10

multiply both sides by 2

35 - 6y = 20

rearranging

-6y = -15

dividing both sides by -6

y = 5/2

The answer for the given polynomial by synthetic division is 3x+16+(30/(x-3)).

Step-by-step explanation:

The given polynomial is (3x^2 +7x -18) divided by (x - 3)

Take (x-3)=0, then x=3

    3  |  3        7       -18  

                    9        48

           3       16       30

step 1: write the coefficients of x^2, x and constant in first row. The divisor 3 is written separately on outside.

step 2: Write down the coefficient of x^2= 3 in the answer row as it is without any change.

step 3: Multiply each number in the answer row with the divisor and fill the answers in the second row.

step 4: The final step is to add the first row and second row. After addition, the answers are written in answer row and the last number in the answer row is the Remainder.

step 5: The remainder is written by dividing it with the divisor (x-3). The answer in the descending powers of x is 3x + 16 + (30/(x-3)).

The result of the division (3x^2 + 7x - 18) by (x - 3) using synthetic division is obtained as (3x + 16 + 30/(x - 3)).

To perform the synthetic division, the divisor (x - 3) is represented by its root '3'. Write down the coefficients from the dividend polynomial (3, 7, -18) at the top of your division setup. Write '3' to the left, leave some space, and then write down '3', '7', -18.

Then, perform the synthetic division: step one, bring the first coefficient (3) straight down. Step two, multiply this number by the root of the divisor (3), which is also 3. Write this product (9) underneath the next coefficient (7). Add these two numbers (7 + 9) to get 16. Write this number under the line. Now, repeat the previous step by multiplying 16 by the root, 3, to get 48. Write this under -18, add to get 30.

The quotient of the division is the polynomials received from the synthetic division which is 3x + 16 with a remainder of 30. So, the result of division (3x^2 + 7x - 18) by (x - 3) is (3x + 16 + 30/(x - 3)).

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Answer:

Step-by-step explanation:

Answer: Here dimension of bigger triangle = 10

Dimension of smaller triangle = 5

Scale factor = 10/5 =2

Therefore

Center C and scale factor 2

Answer:

After 4 days, the temperature will be 3/4 Fahrenheit degrees lower than today

Step-by-step explanation:

Let's calculate the change in temperature after 4 days, this way:

Today's temperature = t in Fahrenheit degrees

Tomorrow's temperature = t - 3/16 Fahrenheit degrees

The day after tomorrow's temperature = t - 2 * 3/16 = t - 3/8 Fahrenheit degrees

Therefore, the temperature after 4 days will be = t - 4 * - 3/16 = t - 3/4 Fahrenheit degrees

After 4 days, the temperature will be 3/4 Fahrenheit degrees lower than today

Answer:

it will always be 1

Step-by-step explanation:

lets make an equation

pick a number : x

add 2 : x+2

multiply by 3 : (x+2)*3

subtract 3 : (x+2)*3-3

divide by 3 : ((x+2)*3-3)/3

if you simplify, you will get 1

step by step simplification

(x+2)*3 = 3x+6

3x+6-3=3x+3

(3x+3)/3 = x+1

x+1-x=1

Final answer:

The algebraic equation for the given math trick is: (((((x + 2) * 3) - 3) / 3) - x).

Explanation:

To represent the math trick you described algebraically, we can use the variable x to represent the initial number you pick. Following the steps you provided, the algebraic equation would be: ((((x + 2) * 3) - 3) / 3) - x. Let's break down each step:

Answer:

f(x) = x³ - 3x² - 10x

Step-by-step explanation:

Given that the zeros are x = - 2, x = 5 and x = 0 then the factors are

(x + 2), (x - 5) and (x - 0) = x

The polynomial is the product of it's factors, thus

f(x) = x(x + 2)(x - 5) ← expand factors using FOIL

     = x(x² - 3x - 10) ← distribute parenthesis by x

     = x³ - 3x² - 10x

Answer: ( -6 , -6.5 )

Step-by-step explanation:

The formula for calculating Mid - point is given by

M = ([tex]\frac{x_{1}+x_{2}}{2}[/tex] , [tex]\frac{y_{1}+y_{2}}{2}[/tex] )

[tex]x_{1}[/tex] = -5

[tex]x_{2}[/tex] = -7

[tex]y_{1}[/tex] = -9

[tex]y_{2}[/tex] = -4

substituting into the formula , we have

M = [tex]\frac{-5-7}{2}[/tex] , [tex]\frac{-9-4}{2}[/tex]

M = [tex]\frac{-12}{2}[/tex] , [tex]\frac{-13}{2}[/tex]

Therefore : mid point = ( -6 , -6.5 )

Answer:

4 11/20

Step-by-step explanation:

The length of road unpaved is 7 3/10 less 2 3/4 miles  The LCD of the fractions is 20 (both 10 and 4 divide evenly into 20).

Thus, the problem becomes 7 6/20 - 2 15/20.

We have to borrow 1 from that 7 because 15/20 is larger than 6/20.  This results in

6 26/20 - 2 15/20, or

4 11/20  

The total length of the main road in Belleville is [tex]7^{(3/10)}[/tex] miles. So far, [tex]2^{3/4}[/tex] miles have been repaved, leaving [tex]7^{(3/10)}[/tex] - [tex]2^{3/4}[/tex] miles that have not been repaved.

1. The total length of the main road is given as [tex]7^{(3/10)}[/tex] miles. In mathematical notation, [tex]7^{(3/10)}[/tex] represents the cube root of 7, which is then raised to the power of 3. So, the total length of the road is the cube root of 7, and then that result is cubed.

2. The length of the repaved portion is given as [tex]2^{3/4}[/tex] miles. In mathematical notation, [tex]2^{3/4}[/tex] represents the fourth root of 2, which is then raised to the power of 3. So, the repaved length is the fourth root of 2, and then that result is cubed.

3. To find the remaining length that has not been repaved, we simply subtract the repaved length from the total length:

  Remaining length = [tex]7^{(3/10)}[/tex] - [tex]2^{3/4}[/tex]

Calculating the values, the total length is approximately 2.262 miles (rounded to three decimal places) and the repaved length is approximately 1.682 miles (rounded to three decimal places). Now, subtracting the repaved length from the total length, we get approximately 0.580 miles (rounded to three decimal places) as the length that has not been repaved.

Therefore, the remaining length that has not been repaved is approximately 0.580 miles (rounded to three decimal places).

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Answer:

He will earn $81 in 12 hours.

Step-by-step explanation:

Given:

Teo earns 47.25$ in 7 hours of work at Beck’s Burgers.

Now, to find the money he will earn in 12 hours.

As, given Teo earns 47.25$ in 7 hours of work.

So, to get the money he will earn in 12 hours we solve by using unitary method:

If Teo earns in 7 hours $47.25.

Then, in 1 hour he earns = [tex]\frac{47.25}{7}[/tex]

Thus, in 12 hours he will earn = [tex]\frac{47.25}{7} \times 12[/tex]

                                                 = [tex]6.75\times 12[/tex]

                                                 =  [tex]\$81.[/tex]

Therefore, he will earn $81 in 12 hours.  

Answer:

The square root of 49 is 7. 7*7=49

Hope this helps,

:)

Step-by-step explanation:

The area of a cirkel is calculated with the formula \pi×r^2. Using the 15 inch radius given we get \pi×15^2=706.5 inches squared.

Answer:

[tex]10 + (\frac{2}{3}) a = 50[/tex] is the CORRECT equation.

Step-by-step explanation:

The given question is INCOMPLETE.

Javier asks his mother how old a tree in their yard is. His mother says, “The sum of 10 and two-thirds of that tree’s age, in years, is equal to 50.” Javier writes the equation { 10 + 2/3} where a is the tree’s age in years. His equation is not correct. What error did he make?

Now here:

a:  The tree’s age in years.

Also,  “The sum of 10 and two-thirds of that tree’s age, in years, is equal to 50.”

⇒ 10 +  two-thirds of that tree’s age  = 50

[tex]\implies 10 + (\frac{2}{3}) a = 50[/tex]

But in the equation written by Javier, the the third fraction is NOT MULTIPLIED by the age of the tree a in Years.

So, the written equation by Javier is Incorrect.

Now, solving the written correct equation for the value of a, we get:

[tex]\implies 10 + (\frac{2}{3}) a = 50\\\implies (\frac{2}{3}) a = 40\\\implies a = 40 \times (\frac{3}{2}) = 60\\\implies a = 60[/tex]

Hence the correct  age of the tree = 60 years

Answer:

12.6

Step-by-step explanation:

plug in 5 for b

5*5 = 25

25-12.4=12.6

Answer:

B= -2.48

Step-by-step explanation:

Divide 5 and -12.4 both by 5 then B=-2.48

In a day, there are 24 hours. Then the number of hours in d days and 6 hours is 24d + 6.

Algebra is the study of mathematical symbols and the rule involves manipulating these mathematical symbols.

The number of hours in d days and 6 hours. Then the algebraic expression will be

We know that in a day, there are 24 hours.

Let the number of the days be d. Then the algebraic expression will be

→ 24 d + 6

Then the number of hours in d days and 6 hours is 24d + 6.

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Answer:

(negative infinity, 2)

Step-by-step explanation:

The two functions are given by f(x) = x - 3 and g(x) = - 0.5x

So, (f - g)(x) = x - 3 - ( - 0.5x) = 1.5x - 3

Then, for (f - g)(x) to be negative (1.5x - 3) < 0

⇒ 1.5x < 3

⇒ x < 2

Therefore, the interval will be (negative infinity, 2) for which the function (f - g)(x) will be negative. (Answer)

Answer:

negative infinity 2

Step-by-step explanation:

just did the test

Answer:

Step-by-step explanation:

12 inch = 1 ft.

12 inch can be be written as (5 + 5 + 2) inch.

It is given that, 5 inches require for 12 beads.

Hence, (12 + 12) = 24 beads will take up (5 + 5) = 10 inches.

There are 2 inches more to fill.

5 inches required for 12 beads.

1 inch required for [tex]\frac{12}{5}[/tex] beads.

2 inches will be required for [tex]\frac{24}{5}[/tex] beads.

[tex]\frac{24}{5} = 4.8[/tex].

Hence, there will 24 + 4 = 28 beads in total. (Only 4 is added instead of 4.8 because, the number can not be in fraction and there is no space for 29 beads in total).

A large box of fruit weighs 18.25 kilograms and a small box weighs 15.5 kilograms.

Step-by-step explanation:

Let,

Weight of large box = x

Weight of small box = y

According to given statement;

4x+8y=197      Eqn 1

2x+3y=83       Eqn 2

Multiplying Eqn 2 by 2

[tex]2(2x+3y=83)\\4x+6y=166\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 1

[tex](4x+8y)-(4x+6y)=197-166\\4x+8y-4x-6y=31\\2y=31[/tex]

Dividing both sides by 2

[tex]\frac{2y}{2}=\frac{31}{2}\\y=15.5[/tex]

Putting y=15.5 in Eqn 2

[tex]2x+3(15.5)=83\\2x+46.5=83 \\2x=83-46.5\\2x=36.5[/tex]

Dividing both sides by 2

[tex]\frac{2x}{2}=\frac{36.5}{2}\\x=18.25[/tex]

A large box of fruit weighs 18.25 kilograms and a small box weighs 15.5 kilograms.

Keywords: linear equation, elimination method

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Answer:

Emily decides marbles the ratio of marbles is 2 to 3 she adds 3 times more to that.

Step-by-step explanation:

Answer:

Step-by-step explanation:

I have 2/3 of milk and I need 6/3 so my neighbor gave me 3