Manuel created a factor tree and wrote the prime factorization of 60 shown below.
A factor tree of 60. 60 branches to 4 and 15. 15 branches to 3 and 5. The equation is 60 = 3 times 4 times 5.
What is Manuel’s error?
He did not include 15 in the prime factorization.
He did not find the prime factors of 4.
He should have started the factor tree with 2 times 30.
He should not have found the factors of 15.

The positive even integers whose sum of reciprocals is 7/24 are 6 and 8.

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

Let the two consecutive even integers be 2x and 2x+2 then there sum of reciprocal will be 7/24 that is now solving for positive value of x by finding roots of quadratic equation :

[tex]\begin{aligned}\frac{1}{2x}+\frac{1}{2x+2}&=\frac{7}{24}\\\frac{1}{x}+\frac{1}{x+1}&=\frac{7}{12}\\\frac{2x+1}{x^2+x}&=\frac{7}{12}\\24x+12&=7x^2+7x\\7x^2-17x+12x&=0\\x&=3, \frac{-4}{7} \end{aligned}[/tex]

Consider only positive value of x that is 3

Therefore, The positive even integers whose sum of reciprocals is 7/24 are 6 and 8.

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Answer:

4x

Step-by-step explanation:

2x+6+2x−6

=2x+6+2x+−6

Combine Like Terms:

=2x+6+2x+−6

=(2x+2x)+(6+−6)

=4x

Answer and explanation:

The equation y=4.2x can be represented by a situation such as the total price of a number of goods

For example, if the total price of chocolate candies purchased from a store is given by the equation

y=4.2x

Such that the price per chocolate candy is $4.2 and x number of chocolate candies are bought, total price of chocolate candies bought is y

If 6 chocolate candies are bought, total price y using the equation would be

y=4.2 *6= $25.2

Answer:

Step-by-step explanation:

product of (2.5 x 10²) x (10⁵)=2.5 x 10⁷

when we multiply the powers we add the 2+5=7

Answer:

9.25×10^7

Step-by-step explanation:

2.5 × 3.7 =9.25 and 10^2+10^5=10^7

Step-by-step explanation:

  Radical already isolated

    √163 = x

Raise both sides to the second power

    (√163)2 = (x)2

    After squaring

    163 = x2  Rearranged equation

    x2  -163 = 0

    This equation has two real roots:

      x1 = ( 0 + sqrt(652) ) / 2 = 12.7671

     x2 = ( 0 - sqrt(652) ) / 2 = -12.7671  Original equation

    √163 = x

    Plug in 12.7671 for  x  

     √163 = (12.7671)

     Simplify

     √163 = 12.767

     Solution checks !!

    Solution is:

     x = 12.7671   Original equation

    √163 = x

    Plug in -12.7671 for  x  

     √163 = (-12.7671)

     Simplify

     √163 = -12.767

     Solution does not check

     12.767 ≠ -12.767

Answer:

x = 30

Step-by-step explanation:

5/6x- 1/5x =19

Get a common denominator of 30

5/6x * 5/5  - 1/5x * 6/6 = 19

25/30x - 6/30x = 19

19/30x = 19

Multiply each side by 30/19

19/30x * 30/19  = 30/19 * 19

x = 30

Answer:

5/6x- 1/5x =19

5/6x- 1/5x =19

?/30x=19

19/30x = 19

x = 19 / 19/30

x = 19 * 30/19

x = 30

Answer:

formulla of perimeter of rectangle

Step-by-step explanation:

perimeter of rectangle=2(l+b)

= 2(7.5+3.25)

=2(11.25)= 22.5

Step-by-step explanation:

l = 7.5cm

b = 3.75cm

perimeter of rectangle = 2(l+b)

= 2(7.5+3.75)

= 2(11.25)

=22.5cm

Answer:

[tex]\angle 6 = 93[/tex]

Step-by-step explanation:

[tex]\angle 5 = 87[/tex] by properties of parallel lines

[tex]\angle 5 + \angle 6 = 180[/tex] because they form a straight angle

[tex]87 + \angle 6 = 180\\\\\angle 6 = 180-87\\\\\angle 6 = 180 - 80 - 7\\\\\angle 6 = 100 - 7\\\\\angle 6 = 93 \longleftarrow[/tex]

Answer:

11/4

Step-by-step explanation:

4/4 is 1 whole.

We have 2 whole.

So, right now we have: 8/4

We can't forget about the 3/4!

8/4+3/4=11/4

This means your total is 11/4

Hope this helps you out!

-AxekickNebulite

The value of an improper fraction of a mixed number [tex]2 \dfrac{3}{4}[/tex] would be [tex]\dfrac{11}{4}[/tex].

Used the concept of the fraction that states that,

A fraction is a part of the whole number and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called a fraction. It can be written in the form of p: q, which is equivalent to p / q.

Given that the mixed number [tex]2 \dfrac{3}{4}[/tex].

Now, change the mixed number [tex]2 \dfrac{3}{4}[/tex]  into an improper fraction as,

[tex]2 \dfrac{3}{4} = \dfrac{(2\times 4 )+ 3}{4}[/tex]

[tex]= \dfrac{11}{4}[/tex]

Therefore, The value of an improper fraction would be [tex]\dfrac{11}{4}[/tex].

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Answer:

points

Step-by-step explanation:

Answer:

Both are correct in certain situations.

Step-by-step explanation:

If the angle between the two given sides is provided, then the triangle is always congruent but if any other angle is provided, the triangle may or may not be congruent.

If a tower casts a shadow 12 m long while a nearby building casts a shadow 8 m long and the building is 16 m high, then the height of the tower is equal to 24 m.

The height of the tower can be determined by using proportionality.

In this problem, the shadows of the building and the tower are proportional to the heights of the building and the tower.

Hence, the equation can be written as:

shadow of the tower ÷ shadow of the building = height of the tower ÷ height of the building

12 / 8 = h / 16

Here h is equal to the height of the tower

1.5 = h / 16

h = 1.5 x 16

h = 24

Hence, the height of the tower is calculated to be 24 meters.

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Answer:

_5x/4 radians is answer

The equilibrium price of hot dogs A. increases.

The equilibrium quantity of hot dogs A. increases

The supply curve shifts right

The demand curve shifts right.

It should be noted that the equilibrium price is the pice at which the quantity demanded and supplied is equal

In this case, the equilibrium price of hot dogs increases and the equilibrium quantity of hot dogs increases.

This will cause a positive affect on the supply and demand curve and they will shift I the right.

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Answer:

y = 17

Step-by-step explanation:

2y + 2 = 3(y - 5)

2y + 2 = 3y - 15

-y = -17

y = 17

Answer:

I believe the answer is C.

Step-by-step explanation:

Hope this helps you.

Answer:

-8b^3ax^2

Step-by-step explanation:

Answer:

0.856p dollars

Step-by-step explanation:

Original price of TV: p

Discount: 20% of p

Discounted price: p - 20% of p = p - 0.2p = 0.8p

7% sales tax on the discounted price of 0.8p: 0.07 * 0.8p = 0.056p

Add the 7% tax to the discounted price: 0.8p + 0.056p = 0.856p

Answer: 0.856p dollars

Answer:

  Change on Day 1 = 29.80 °C

  Change on Day 2= 30.60 °C

  the most change occurred on Day 2

Step-by-step explanation:

Given a table of days and temperatures, you are asked for the changes each day, and you are asked which day changed the most.

In general, the change in an amount is the difference between the final amount and the beginning amount. Here we have temperatures at the beginning of the day and the end of the day. We presume the change of interest is the difference between the temperature at the end of the day and that at the beginning.

  end of day temp - beginning temp = 18.74 -(-11.06) = 29.80 . . . °C

  end of day temp - beginning temp = 21.29 -(-9.31) = 30.60 . . . °C

The day 2 change is larger than the day 1 change, so the most change occurred on day 2.

Answer:

no, real numbers do not have first numbers.

Step-by-step explanation:

There are also more complicated number systems than the real numbers, such as the complex numbers. Every real number is a complex number, but not every complex number is a real number. Similarly, 3/7 is a rational number but not an integer.

Answer:

Step-by-step explanation:

y = 4x + 2                 Substitute x = -6

y = 4(-6) + 2

y = -24 + 2

y = - 22

Answer:

x=5.6

Step-by-step explanation:

The equation is

2/1.6=7/x

1.25=7/x

1.25x=7

x=7/1.25

x=5.6

Answer:

Step-by-step explanation:

We will use a proportion to solve this. All we need are two corresponding values. One is x and 7, we'll pick the other as 32 and 4.

Now, we'll set up the proportion

[tex]\frac{x}{7} = \frac{32}{4}[/tex]

To solve a proportion, we cross multiply the means and extremes.

4x = 32 x 7

4x = 224

x = 56

We can check the proportion by substituting our answer in for x and seeing if the products equal. If they do, we know we have the correct answer.

4(56) = 32 x 7

224 = 224 ✅

Answer:

Step-by-step explanation:

The distance from the balcony to the ground level = 37 - 0 = 37ft

The distance from the basement floor to the ground level = 0 - (-17) = 17 feet

the distance of the balcony and basement from ground level will be the sum of the distances gotten = 37 - (-17)

= 37 + 17

= 54 feet

Hence the distance of the balcony and basement from ground level is 54 feet

Answer:

my acc just got yeeted by a penguin pfp

Step-by-step explanation:

Answer:

oops look in commments

Step-by-step explanation:

Answer:

719

Step-by-step explanation:

addition yes

Answer:719 bags

Step-by-step explanation:

Add:642+50+22=714

Then add 714+5=719

Answer:

The sum of the exterior angles in a convex 50-gon polygon is 360° ⇒ A

Step-by-step explanation:

In the question

∵ The polygon has 50 sides

→ By using the 3rd rule above

∵ The sum of the exterior angles of any polygon (n-gon) is 360°

∴ The sum of the exterior angles in a convex 50-gon polygon is 360°

Answer:

Step-by-step explanation: