tim and his brother are building towers out of blocks. Tim is using blue blocks that are 6 cm tall and his brother is using green blocks that are 8 cm tall. They both made towers the same height. What is the shortest possible height of the tower? how many of each color block did they use

Answer:

8

Step-by-step explanation:

To solve this, you can add 2/5 b to both sides of the equation. You now have 3 + 5/5 (or 1) b = 11. => 3 + b = 11 => Now, subtract 3 from both sides, and you have b = 11 - 3, and then b = 8.

Step-by-step explanation:

3 + 2/5 b =11 - 2/5 b (this is the given question is it?)

2/5 b + 2/5 b= 11 - 3 (like terms together, you transpose -2/5b to the other side as shown.)

2b+2b = 8 ( at that stage you would find t

5 hat 5 is the common value to go into 5 itself, as shown.

4b = 8 ( you just add 2b + 2b to have 4b)

5

4b = 8 ( at that point you cross multiply

5 1 as shown)

4b = 8 × 5 ( simple math as shown)

4b = 40 ( you multiply 8 × 5 to obtain 40)

b =10 you can prove that. Thank you.

Option B is correct. The required composite function where f(g(x)) is x is f (x) = StartFraction 2 Over x EndFraction and g (x) = StartFraction 2 Over x EndFraction

Composite functions are functions written inside another function e.g f(g(x))

Given the expressions

f(x) = 2/x

g(x) = 2/x

We are to find the composite function f(g(x))

f(g(x)) = f(2/x)

f(2/x) =  (2/(2/x))

f(2/x)  = 2 * x/2

f(2/x) = x

Hence the required composite function where f(g(x)) is x is f (x) = StartFraction 2 Over x EndFraction and g (x) = StartFraction 2 Over x EndFraction

[tex]1. \( (f \circ g)(x) = \frac{1}{x^2} \)\\2. \( (f \circ g)(x) = x \)\\3. \( (f \circ g)(x) = -x \)\\4. \( (f \circ g)(x) = \frac{1}{4}x - 1 \)[/tex]

let's break down each pair of functions and find their composition:

1. For [tex]\( f(x) = x^2 \) and \( g(x) = \frac{1}{x} \):[/tex]

  To find [tex]\( (f \circ g)(x) \)[/tex], we substitute [tex]\( g(x) \) into \( f(x) \):[/tex]

  [tex]\[ (f \circ g)(x) = f(g(x)) = f\left(\frac{1}{x}\right) = \left(\frac{1}{x}\right)^2 = \frac{1}{x^2} \][/tex]

  So, [tex]\( (f \circ g)(x) = \frac{1}{x^2} \).[/tex]

2. For [tex]\( f(x) = \frac{2}{x} \) and \( g(x) = \frac{2}{x} \):[/tex]

  Here, [tex]\( (f \circ g)(x) = f(g(x)) = f\left(\frac{2}{x}\right) \).[/tex]

  When you substitute [tex]\( \frac{2}{x} \) into \( f(x) \),[/tex]  you get:

 [tex]\[ (f \circ g)(x) = f\left(\frac{2}{x}\right) = \frac{2}{\frac{2}{x}} = x \][/tex]

  So, [tex]\( (f \circ g)(x) = x \).[/tex]

3. For [tex]\( f(x) = \frac{x-2}{3} \) and \( g(x) = 2 - 3x \):[/tex]

 [tex]\( (f \circ g)(x) = f(g(x)) = f(2 - 3x) \).[/tex]

  Substituting  [tex]\( 2 - 3x \) into \( f(x) \),[/tex]we get:

 [tex]\[ (f \circ g)(x) = f(2 - 3x) = \frac{(2 - 3x) - 2}{3} = \frac{-3x}{3} = -x \][/tex]

  So, [tex]\( (f \circ g)(x) = -x \).[/tex]

4. For [tex]\( f(x) = \frac{1}{2}x - 2 \) and \( g(x) = \frac{1}{2}x + 2 \):[/tex]

  Here, [tex]\( (f \circ g)(x) = f(g(x)) = f\left(\frac{1}{2}x + 2\right) \).[/tex]

  When you substitute [tex]\( \frac{1}{2}x + 2 \) into \( f(x) \),[/tex] you get:

 [tex]\[ (f \circ g)(x) = f\left(\frac{1}{2}x + 2\right) = \frac{1}{2}\left(\frac{1}{2}x + 2\right) - 2 = \frac{1}{4}x + 1 - 2 = \frac{1}{4}x - 1 \][/tex]

  So, [tex]\( (f \circ g)(x) = \frac{1}{4}x - 1 \).[/tex]

So, summarizing:

1. For [tex]\( f(x) = x^2 \) and \( g(x) = \frac{1}{x} \), \( (f \circ g)(x) = \frac{1}{x^2} \).[/tex]

2. For [tex]\( f(x) = \frac{2}{x} \) and \( g(x) = \frac{2}{x} \), \( (f \circ g)(x) = x \).[/tex]

3. For [tex]\( f(x) = \frac{x-2}{3} \) and \( g(x) = 2 - 3x \), \( (f \circ g)(x) = -x \).[/tex]

4. For [tex]\( f(x) = \frac{1}{2}x - 2 \) and \( g(x) = \frac{1}{2}x + 2 \), \( (f \circ g)(x) = \frac{1}{4}x - 1 \).[/tex]

Answer:

Step-by-step explanation:

                                        Solving equation A: y = x

Let us consider the given equation A:

                                                      y = x

y = x

y = 1    ∵ x = 1

Hence, (1, 1) is the ordered pair of  y = x

y = x

y = 2    ∵ x = 2

Hence, (2, 2) is the ordered pair of  y = x

y = x

y = 3    ∵ x = 3

Hence, (3, 3) is the ordered pair of  y = x

y = x

y = 4    ∵ x = 4

Hence, (4, 4) is the ordered pair of  y = x

y = x

y = 5    ∵ x = 5

Hence, (5, 5) is the ordered pair of y = x

Lets us consider all the ordered pairs i.e. (1, 1), (2, 2), (3, 3), (4, 4) and (5, 5) to make a table for y = x.

y                 x

1                  1

2                 2

3                 3

4                 4

5                 5

As from the table, lets take the ratio of every point i.e. y/x

Hence, the ratio for all the points on the equation y = x is same. Hence, the equation y = x REPRESENTS a proportional relationship. Please also check the graph in attached figure a.

                                          Solving equation A: y = x +2

Let us consider the given equation A:

                                                         y = x + 2    

y = x + 2

y = 1 + 2 ⇒ 3  ∵ x = 1

Hence, (1, 3) is the ordered pair of y = x + 2

y = x + 2

y = 2 +2 ⇒ 4   ∵ x = 2

Hence, (2, 4) is the ordered pair of y = x + 2

y = x + 2

y = 3 + 2 ⇒ 5    ∵ x = 3

Hence, (3, 5) is the ordered pair of  y = x + 2

y = x + 2  

y = 4 + 2 ⇒ 6   ∵ x = 4

Hence, (4, 6) is the ordered pair of  y = x + 2

y = x + 2

y = 5 +2 ⇒ 7    ∵ x = 5

Hence, (5, 7) is the ordered pair of y = x + 2

Lets us consider all the ordered pairs i.e. (1, 3), (2, 4), (3, 5), (4, 6) and (5, 7) to make a table for y = x + 2.

y                 x + 2

1                  3

2                 4

3                 5

4                 6

5                 7

As from the table, lets take the ratio of every point i.e. y/x

Hence, the ratio for all the points on the equation y = x+2 is not same. Hence, the equation y = x + 2 DOES NOT REPRESENT a proportional relationship. Please also check the graph in attached figure a.

Keywords: equation, graph

Learn more equation and graphs from brainly.com/question/12767017

#learnwithBrainly

Irene's list of factors for the number 88 is almost correct, but she forgot to include the number 1.

Irene wants to list the factors for 88 and she writes 2, 4, 8, 11, 22, 44, and 88. To verify if Irene is correct, we need to identify all of the numbers that can evenly divide 88 without leaving a remainder. Starting with the number 1, which is a factor of every number:

1 x 88 = 88, so 1 and 88 are factors.

2 x 44 = 88, so 2 and 44 are factors.

4 x 22 = 88, so 4 and 22 are factors.

8 x 11 = 88, so 8 and 11 are factors.

Since there are no other numbers between 1 and 88 that can multiply together to equal 88, the list that Irene wrote appears to be missing the number 1.

Therefore, Irene's list is almost correct, but for it to be complete, it should include the number 1. The full list of factors for the number 88 should be 1, 2, 4, 8, 11, 22, 44, 88.

Answer:

Its 24 and 12

Step-by-step explanation:

Answer:

He's right

Step-by-step explanation:

Answer:

1. The percent commission earned is 3%.

2. The loan period is 3.29 years.

Step-by-step explanation:

1. Salesman has $65,100 in sales. He earned $1,953 in commission.

Let the percent commission earn be x%

Therefore, x% of the sales equals $1,953

[tex]\frac{x}{100} of  $65,100 = $1,953[/tex]

[tex]\frac{x}{100}  * 65100 = 1953\\\frac{65100x}{100} = 1953[/tex]

We cross multiply

[tex]\frac{65100x}{100}  = 1953\\65100x = 1953 * 100\\65100x = 195300[/tex]

Divide both side by the coefficient of 'x' (65100)

[tex]\frac{65100x}{65100} =  \frac{195300}{65100} \\x = 3[/tex]

Therefore, the percent commission earned is 3%

2. Interest (I) = $299  Principal (P) = $1300   Rate (R) = 7%

The formula for finding interest is given as: [tex]I = \frac{PRT}{100}[/tex]

Therefore, substituting into the formula, we have:

[tex]299 = \frac{1300 * 7 * T}{100}[/tex]

We are finding the time it takes the loan to earn an interest of $299

[tex]299 = \frac{1300 * 7 * T}{100} \\299 = \frac{9100T}{100}[/tex]

We cross-multiply:

[tex]299 * 100 = 9100T\\29900 = 9100T[/tex]

Divide both side by the coefficient of T (9100)

[tex]\frac{29900}{9100}  = \frac{9100T}{9100}\\T = 3.29[/tex]

Therefore, the time taken for the loan to earn such interest is approximately 3.29 years

Answer:

-19

Step-by-step explanation:

4x-8(2-x)

4x-16+8x

12x-16

12(-1/4)-16

-12/4-16

-3-16

-19

Answer:

-19 I think lemme know if im right

Step-by-step explanation:

Answer:  [tex]m=0[/tex]

Step-by-step explanation:

The slope can be calculated with this formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Notice that the formula shows the change in "y" for a unit change in "x"  on the line.

In order to solve this exercise, it is important to remember that:

1. If a line is increasing, then its slope is positive.

2. If a line is decreasing, then its slope is negative.

3. If the line is horizontal, its slope is zero.

4. If the line is vertical, it has no slope.

Therefore, since the given line that passes through the point [tex](3,-4)[/tex], is horizontal, its slope is:

[tex]m=0[/tex]

For 5 games, the cost will be equal for each option.

Step-by-step explanation:

Given,

Lane rental of offer A = $20

Per game charges = $3

Let,

x be the number of games.

A(x) = 3x + 20

Lane rental is $35 for maximum 10 games.

B(x) = 35

For the cost to be same;

A(x) = B(x)

[tex]3x+20=35\\3x=35-20\\3x=15[/tex]

Dividing both sides by 3

[tex]\frac{3x}{3}=\frac{15}{3}\\x=5[/tex]

For 5 games, the cost will be equal for each option.

Keywords: function, division

Learn more about functions at:

#LearnwithBrainly

Answer:

C

Step-by-step explanation:

The diagonal of the square creates 2 right triangles with the diagonal as the hypotenuse.

Using Pythagoras' identity in either of the right triangles.

The square on the hypotenuse is equal to the sum of the squares of the other 2 sides.

Let x be the side of the square, then

x² + x² = 40², that is

2x² = 1600 ( divide both sides by 2 )

x² = 800 ( take the square root of both sides )

x = [tex]\sqrt{800}[/tex]

  = [tex]\sqrt{100(8)}[/tex]

=  = 10[tex]\sqrt{8}[/tex]

  = 10 × [tex]\sqrt{4(2)}[/tex]

  = 10 × 2[tex]\sqrt{2}[/tex] = 20[tex]\sqrt{2}[/tex] → C

Answer:

It is because a triangle has a total angle sum of 180 degrees.

Step-by-step explanation:

90+90=180

But that was only 2 corners so the last corner has to be 0 degrees which is impossible.

Answer: A triangle does not contain two right angles.

.

Step-by-step explanation:

Answer:

1.14

Step-by-step explanation:

hundreth = 0.01

so we ignore the 3 because it is in teh thousandths

hope this helps :)

The equation of the line which is perpendicular to the line 4x + 3y = 9 and passes through the point (-2,3) is y = 3/4x + 4.5.

The original equation is 4x + 3y = 9. To start off, rewrite this equation in slope-intercept form (y = mx + b) to help find the slope. After isolating y, the equation turns into y = -4/3x + 3. So, the slope of the original line is -4/3.

Perpendicular lines have slopes which are negative reciprocals of each other, thus the slope of the line perpendicular to the given line is the negative reciprocal of -4/3, which is 3/4 (m = 3/4 for the second line)

We are also given that the line we are looking for passes through the point (-2,3). Use the point-slope form of a line, given by y - y1 = m(x - x1), where m is the slope, and (x1, y1) is the given point. Substituting in the values, you get:

y - 3 = 3/4(x - -2).

Simplifying the equation, we find that the line perpendicular to 4x + 3y = 9 and passing through (-2, 3) is y = 3/4x + 4.5

https://brainly.com/question/18271653

#SPJ12

Final answer:

To find the total weight in Robbie's backpack, the weights of the history textbook (2 5/6 pounds) and lunch (1 2/3 pounds) are added, resulting in a total of 4 1/2 pounds.

Explanation:

The question involves finding the total weight of items in Robbie's backpack: a history textbook and his lunch. The history textbook weighs 2 5/6 pounds and his lunch weighs 1 2/3 pounds.

To find the total weight, we first convert the mixed numbers into improper fractions for easier addition. The history textbook's weight as an improper fraction is (2×6)+5 = 17/6 pounds. The lunch's weight is (1×3)+2 = 5/3 pounds.

Adding these two fractions gives us:

   17/6 + 5/3 = 17/6 + 10/6 = 27/6 pounds

Since 27/6 simplifies to 4 1/2 pounds, the total weight in Robbie's backpack is 4 1/2 pounds.

Answer:

(B) 2(x+5)(x−5)

Explanation:

Factor 2x²−50

2(x+5)(x−5)

Answer:

b) 2(x - 5)(x + 5)

Step-by-step explanation:

2x² - 50

2(x² - 25)

(x² - 25) is a difference of squares and it equals (x - 5)(x + 5)

So the answer is;

2(x - 5)(x + 5)

Answer:

Out of every 5 trials, the desired outcome will occur approximately 2 times

Step-by-step explanation:

The first statements states that it will happen exactly two times, but probability never guarantee the outcome

The third and fourth statement states out of 7 which cannot be true as 2-5 basically means out of 5

Answer:

B: Out of every 5 trials, the desired outcome will occur approximately 2 times.

Step-by-step explanation:

Answer: B. 42 inches

Step-by-step explanation:

Answer:

42 inches

Step-by-step explanation:

The function states in its second row that for size 2, the range of x (a child’s height in inches) is 42 ≤ x < 44. Then, the option 41.9 is incorrect because is less than 42 and x is greater-or-equal-to 42; option 44 inches is incorrect because it is equal to 44 and the equality sign is not included; option 44.1 inches is greater than 44 and x is less than 44; and option 42 inches is correct  because x is greater-than-or-equal to 42, that is, the equal sign is included.

Answer:

About $90, because the trend line shows that value for $11.

Step-by-step explanation:

It is the only one that shows a constant rate of change.

Answer:

the first one ( the line closest to 90)

Step-by-step explanation:

Answer:

.19 cent per egg

Step-by-step explanation:

15*12=180

34.20/180= .19

The unit cost per egg is $0.60 when a case of eggs costs $34.20.

The unit cost per egg is $0.60.

To find the cost per egg when a case contains 15 dozen eggs costing $34.20, you first calculate the cost per dozen by dividing the total cost by the number of dozens (15). Then, you divide the cost per dozen by 12 to find the cost per egg. In this case, $34.20 divided by 15 gives $2.28 cost per dozen. Finally, $2.28 divided by 12 equals $0.60, so each egg costs $0.60.

Length of diameter is 2.86 cm

Solution:

Given that circumference of a circle is 8.97 cm

To find: length of diameter

We can use the formula for circumference of circle to find radius and then we can find diameter

The circumference of circle is given as:

[tex]C = 2 \pi r[/tex]

Where "r" is the radius of circle and [tex]\pi[/tex] is a constant equals to 3.14

Substituting c = 8.97 and [tex]\pi = 3.14[/tex]

[tex]8.97 = 2 \times 3.14 \times r\\\\8.97 = 6.28 \times r\\\\r = \frac{8.97}{6.28}\\\\r = 1.4283[/tex]

Thus radius of circle is 1.4283 cm

Finding diameter of circle

diameter = 2(radius)

diameter = 2(1.4283) = 2.8566

On rounding to two decimal point we get, 2.86

Thus length of diameter is 2.86 cm

Answer:

We can say that equations 1 and 2 have no solutions.

Step-by-step explanation:

The equation 1 is |3x − 1| + 7 = 2 ........ (1)

⇒ |3x − 1| = - 5

This equation is invalid as the absolute value of (3x - 1) will always be positive and here it is - 5.

Therefore, this above equation has no solution.

The equation 2 is |2x + 1| + 4 = 3 ........ (2)

⇒ |2x + 1| = - 1

This equation is invalid as the absolute value of (2x + 1) will always be positive and here it is - 1.

Therefore, this above equation has no solution.

Hence, we can say that equations 1 and 2 have no solutions. (Answer)

Answer:

24

Step-by-step explanation:

y/4-9=-3

y/4=-3+9

y/4=6

y=6*4

y=24

Answer:

True

Step-by-step explanation:

1 and 3 are vertical angles

Answer: False

<1 and <3 are Supplementary Angles

Step-by-step explanation:

Answer:

The answer is C. y=cos(0.4x)

Step-by-step explanation:

took the test

Answer: c

Step-by-step explanation:

y=cos(0.4x)

You paid 22% gratuity at the restaurant.

Step-by-step explanation:

Given,

Amount of bill = $59

Amount paid = $72

Gratuity = Amount paid - Amount of bill

Gratuity = 72 - 59 = $13

Gratuity percentage = [tex]\frac{Gratuity}{Amount\ of\ bill}*100[/tex]

Gratuity percentage = [tex]\frac{13}{59}*100=\frac{1300}{59}[/tex]

Gratuity percentage = 22.03%

Rounding off to whole percent

Gratuity percentage = 22%

You paid 22% gratuity at the restaurant.

Keywords: percentage, subtraction

Learn more about subtraction at:

#LearnwithBrainly

The percentage did you pay is 22.03%

Given that,

Based on the above information, the calculation is as follows:

[tex]= (\$72 - \$59) \div (\$59)\\\\= \$13 \div \$59[/tex]

= 22.03%

Learn more: https://brainly.com/question/1289629?referrer=searchResults

Answer:getting rid of the constant

Step-by-step explanation:

Answer: simplify x + 7 = 2x + 5 - 4x by combining like terms so x+7= 5-2x

Step-by-step explanation:

Answer:

The area of the circle is 3,8550 mm

Step-by-step explanation:

Diameter    (d) = 70 mm

Radius             (r) = (70/2) mm = 35mm

Π                   = 22/7

Area of circle x       =   πr^2

                  =   22/7 x 35^2

                  =   22/7 x 1225

                  =   26,950/7

                  =   3,850 mm

Answer:

90π units²

Step-by-step explanation:

(refer to attached)

Total Surface are off a right cylinder = area of its ends + area of curved surface

Given radius, r = 3 units and height, h = 12 units

Area of 2 ends,

= Area of 2 circles

= 2 x πr²

= 2π (3²)

= 2π (9)

=18π units²

Area of curved surface,

= 2πrh

= 2π(3)(12)

= 72π units²

Hence,

Surface area = 18π + 72π = 90π units²

The solution is, 90π units² is its surface area.

Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

here, we have,

given that,

A right cylinder has a radius of 3 and a height of 12.

we know that,

Total Surface are off a right cylinder = area of its ends + area of curved surface

Given radius,

r = 3 units and height, h = 12 units

Area of 2 ends,

= Area of 2 circles

= 2 x πr²

= 2π (3²)

= 2π (9)

=18π units²

Area of curved surface,

= 2πrh

= 2π(3)(12)

= 72π units²

Hence,

Surface area = 18π + 72π = 90π units²

To learn more on Area click:

brainly.com/question/20693059

#SPJ7

Answer:

The volume of sphere is 1436.03 inches³.

Step-by-step explanation:

Given:

The radius of sphere = 7 inches.

Now, to find the volume.

So, to get the volume we put the formula:

[tex]Volume=\frac{4}{3} \pi r^3[/tex]

Taking the value of π = 3.14

[tex]Volume=\frac{4}{3}\times 3.14\times {7}^3[/tex]

[tex]Volume=\frac{4}{3}\times 3.14\times 343[/tex]

[tex]Volume=\frac{4}{3}\times 1077.02[/tex]

[tex]Volume=\frac{4308.08}{3}[/tex]

[tex]Volume=1436.03\ inches^3[/tex]

Therefore, the volume of sphere is 1436.03 inches³.

Step-by-step explanation: To find the volume of the sphere, start with the formula for the volume of a sphere.

Volume = [tex]\frac{4}{3} \pi r^{3}[/tex]

Notice that our sphere has a radius of 7 inches so plugging into the formula, we have [tex](\frac{4}{3})(\pi)(7 in.)^{3}[/tex].

Start by simplifying the exponent. (7 in.)³ is equal to 7 inches x 7 inches x 7 inches or 343 in³ so we have [tex](\frac{4}{3}) (343 in.^{3})(\pi)[/tex].

Next, 4 x 343 is 1,372 which gives us [tex]\frac{1,372\pi }{3}[/tex]. Notice that 1,372 doesn't divide by 3 so this is our final answer for the volume of the sphere.