It takes 9 builders 54 days to complete a house.

How long would it take 6 builders to complete the same house?

Hi there.

[tex]= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =[/tex]

What we should do here is multiply the fractions. We know this information because it says in our problem - "the product".

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If ever we come across the word "the product of" in any mathematics problems, we should know that the operation we should use is "multiplication".

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This is how we multiply fractions:

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First, we check: Is there any way we can reduce the fractions?

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We cannot divide the top and bottom of these two fractions by the same number, but there is some reducing that can be done:

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Notice that 4 and 8 have a common factor - 2.

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Since 4 and 8 have a 2 in common, we divide 8 and 4 by 2:

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[tex]\bf{\displaystyle\frac{4}{15} *\frac{3}{8}}[/tex]

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[tex]\bf{\displaystyle\frac{1}{15} *\frac{3}{2}}[/tex]

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Now, 15 and 3 also have a common factor - 3:

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[tex]\bf{\displaystyle\frac{1}{5} *\frac{1}{2}}[/tex]

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What we should do now is multiply 1 by 1 and 5 times 2:

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[tex]\bf{\displaystyle\frac{1}{10}}[/tex]

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I hope that this helps clear your doubts; if any are left, please ask.

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I wish you a nice rest of your day.

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[tex]\bf{W}\sf{r}\bf{i}\sf{t}\bf{i}\bf{n}\sf{g}\:\bf{A\:\sf{L}\bf{e}\sf{t}\bf{t}\sf{e}\bf{r}.[/tex]

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[tex]\huge\textbf{What does \boxed{product} mean?}[/tex]
[tex]\bullet\large\text{ Product simply means multiplication/multiply}[/tex]

[tex]\huge\textbf{So, what are we doing in the equation?}[/tex]

[tex]\bullet\large\text{ We are multiplying! :)}[/tex]

[tex]\huge\textbf{What should our equation look like?}[/tex]

[tex]\rm{\dfrac{4}{15}\times\dfrac{3}{8}}[/tex]

[tex]\huge\textbf{What are the steps?}[/tex]

[tex]\mathsf{\dfrac{4}{15}\times\dfrac{3}{8}}[/tex]

[tex]\mathsf{= \dfrac{4\times 3}{15\times 8}}[/tex]

[tex]\mathsf{= \dfrac{12}{120}}[/tex]

[tex]\mathsf{= \dfrac{12\div2}{120\div2}}[/tex]

[tex]\mathsf{= \dfrac{6}{60}}[/tex]

[tex]\mathsf{= \dfrac{6\div3}{60\div3}}[/tex]

[tex]\mathsf{= \dfrac{2}{20}}[/tex]

[tex]\mathsf{= \dfrac{2\div2}{20\div2}}[/tex]

[tex]\mathsf{= \dfrac{1}{10}}[/tex]

[tex]\huge\textbf{What is your answer to the question?}[/tex]

[tex]\huge\boxed{\mathsf{\dfrac{1}{10}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Height be h

[tex]\\ \rm\Rrightarrow tan\Theta=\dfrac{Perpendicular}{Base}[/tex]

[tex]\\ \rm\Rrightarrow tan54=\dfrac{h}{60}[/tex]

[tex]\\ \rm\Rrightarrow h=60tan54[/tex]

[tex]\\ \rm\Rrightarrow h=82.6\approx 83m[/tex]

Answer:

83 m  (nearest metre)

Step-by-step explanation:

This can be modeled as a right triangle, where the base is 60 m and the height is the height of the building.

Alternate Interior Angles Theorem (Z-angles)

If a line intersects a set of parallel lines in the same plane at two distinct points, the alternate interior angles that are formed are congruent.

Using the Alternate Interior Angles theorem, the angle between the ground and the dashed line (angle of elevation) is 54°.

Tan trigonometric ratio

[tex]\sf \tan(\theta)=\dfrac{O}{A}[/tex]

where:

Given:

Substituting the given values into the formula and solving for h:

[tex]\implies \sf \tan(54^{\circ})=\dfrac{h}{60}[/tex]

[tex]\implies \sf h=60 \tan(54^{\circ})[/tex]

[tex]\implies \sf h=82.58291523...[/tex]

[tex]\implies \sf h=83\:\:m\:(nearest\:metre)[/tex]

Answer:

the Area = 100in^2

Step-by-step explanation:

pls mark brainiest

Area of triangle is 10 square cm.

The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.

Given

Base = 4

Height = 5

Area of triangle = [tex]\frac{1}{2}[/tex] × b × h

=  [tex]\frac{1}{2}[/tex] × 4 × 5

= 2 × 5

= 10

Hence, area of triangle is 10 square cm.

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The rationalization the denominator of the fraction  (6)/(4+\sqrt(5)) is [tex]\dfrac{6(4-\sqrt(5))}{11}[/tex].

Suppose the given fraction is [tex]\dfrac{a}{b+c}[/tex]

Then the conjugate of the denominator is given by b - c

Thus, rationalizing the fraction will give us

[tex]\dfrac{a}{b+c} \times \dfrac{b-c}{b-c} = \dfrac{a(b-c)}{b^2 - c^2}[/tex]

The given expression is

[tex]\dfrac{6}{4+\sqrt(5)}\\\\[/tex]

By rationalizing the denominator of the fraction

[tex]\dfrac{6}{4+\sqrt(5)}\times \dfrac{4-\sqrt(5)}{4-\sqrt(5)} \\\\\\\dfrac{6(4-\sqrt(5))}{4^2-(5)}\\\\\\\dfrac{6(4-\sqrt(5))}{11}[/tex]

Thus, the rationalization the denominator of the fraction  (6)/(4+\sqrt(5)) is [tex]\dfrac{6(4-\sqrt(5))}{11}[/tex].

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Answer:

3

Step-by-step explanation:

because there are only three pictures

Find answers to the questions in the attached file.

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Answer:

37.5°, 52.5°

Step-by-step explanation:

Let the two angles be 5x and 7x

Total ratio= 5+7 =12

5x = (5/12) ×90° ( sum of complementary angles = 90°)

= (5/2)×15°

75/2= 37.5°

Similarly

7x = (7/2)×15°

=105/2= 52.5°

37.5°+52.5°=90° (sum of complementary angles= 90°)

Answer:

(3)+1. 12-2=9+1 so 9 is the answer

By conservation of momentum, we will see that the mass of Gru is 32 kilograms.

Here we need to use the conservation of momentum.

Initially, Gru is stop, and Agnes with a mass of 30kg has a velocity of 1.2 m/s, so the total initial momentum is:

P = 30kg*1.2m/s = 36 kg*m/s.

At the end, the total mass is M, the mass of Gru, plus the mass of Agnes:

(M + 30kg).

And the final speed is 0.5 m/s, then the final momentum is:

P' = (M + 30kg)*0.5m/s

And the final momentum must be equal to the initial momentum:

36 kg*m/s =  (M + 30kg)*0.5m/s

Now we can solve that for M:

( 36 kg*m/s)/(0.5 m/s) = M + 30kg

72kg = M + 30kg

72kg - 30kg = 32 kg = M

The mass of Gru is 32 kilograms.

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The height and the base area of both the design must be equal. Then the correct option is A.

A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.

A manufacturer of kitchen utensils and gadgets is considering changing the design of their salt and pepper shakers.

Their current design is a standard cylinder, while the new design they are considering is an oblique cylinder.

The figure shows both designs.

The volume of the cylinder will be given as

V = πr² h

If the volume of the oblique cylinder and right cylinder is the same.

Then the height of both the designs must be equal and the base area of both the design must be equal.

Then the correct option is A.

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Answer:

D

Step-by-step explanation:

did the test on edmentum

Answer:

5 hours

Step-by-step explanation:

Mark recieves 3mg per hour. This can be rewritten as y=3x. Cassie recieves 2x+5. To solve, use substitiution. 3x=2x+5. To solve, subtract "2x" from "3x." You then get x=5.

Answer:

14 divided by 9 = 1.5

The result of 14/9 is a non-terminating, repeating decimal.

Answer:

1.56 [?]

this question's wording was slightly confusing but I think this is what you meant

Step-by-step explanation:

by dividing the two numbers, (you can use long division or a calculator) while they are not in a fraction state (don't rewrite it as [tex]\frac{14}{9}[/tex], actually divide

14 by 9) you will end up with a number:

1.55555556

(repeating decimal)

So, you can either write this as 1.5 with a little dash over the 5

Or, you can round the decimal to 1.56 .

(method: by actual division)

The midpoint theorem simply states that the line segment that joins the two sides of the triangle is parallel to the third side.

Your information is incomplete. Therefore, an overview of the theorem will be given. It should be noted that the midpoint theorem states that the line drawn through the mid point of one side of the triangle is parallel to another side.

To find the midpoint, one can measure the distance between the two end points and divide the results by 2.

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Answer:

here ....x = 2 and y = 3

[tex] = xy - y + x \times x[/tex]

[tex] = 2 \times 3 - 3 + 2 + 2 \times 2[/tex]

[tex] = 6 - 3 + 2 + 4[/tex]

[tex] = 12 - 3[/tex]

[tex] = 9[/tex]

To write this sum as a fraction, you can use the following formula: 5x/4 + 3/4.

To transform a fraction into a sum we must perform the following procedure:

According to the above, all we have to do is divide the fraction using each digit of the numerator and put the same denominator.

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Answer:

26

Step-by-step explanation:

You would add the 3 numbers and then minus that from 100

Answer:

A. -1/8 x + 3/16

Step-by-step explanation:

Distribute -1/2 over the parentheses

-1/2 ( 1/4 x - 3/8 )

-1/2 (1/4 x) - 1/2 (-3/8 )

multiply fractions to simplify

-1/8 x + 3/16

A is correct

Answer:

Step-by-step explanation:

  base = b = 7  km

  altitude or height = h = 3.8 km

     [tex]\sf \boxed{\text{\bf Area of triangle =$\dfrac{1}{2}b*h$ }}[/tex]

                                    [tex]= \dfrac{1}{2}*7*3.8\\\\= 7 * 1.9\\\\= 13.3 \ km^2[/tex]

     length = l = 8.2 cm

     width  = w = 7 cm

      [tex]\sf \boxed{\text{\bf Area of rectangle = l*w}}[/tex]

                                        = 8.2 * 7

                                        = 57.4 cm²

            base = b = 9.1 km

           height = h = 5 km

[tex]\sf \boxed{\text{\bf Area of parallellogram =b*h}}[/tex]

                                          = 9.1 * 5

                                          = 45.5 km²

           Parallel sides a = 8.9 m  & b =  2.7 m

           height = h = 4.2 m

[tex]\sf \boxed{\text{\bf Area of trapezium =$\dfrac{(a +b)*h}{2}$}}[/tex]

                                   [tex]\sf =\dfrac{(8.9+2.7)*4.2}{2}\\\\=\dfrac{11.6*4.2}{2}\\\\= 5.8 * 4.2\\\\= 24.36 \ m^2[/tex]

Answer:  

1# 13.3 Km

2# 57.4 Km

3# 45.5 Km

4# 24.36 Km

Answer: C

Step-by-step explanation:

[tex]16x+8 \geq 12x+20\\ \\ 4x+8 \geq 20\\ \\ 4x \geq 12\\ \\ \boxed{x \geq 3}[/tex]

Answer:

Question 13 of 16 Evaluate the following function at the values 2, -4, and x-1. f(x)=x2-5 = ..... f(2)= (Type an integer or a simplified fraction.) f(-4)=L(Type an integer or a simplified fraction.) f(x-1)= (Simplify your answer. Type an expression using x as the variable. Use integers or fractions for any numbers in the expression.)

Answer:

The second picture is the correct answer the graph must be decreasing..

Step-by-step explanation:

The second picture is the correct answer the graph must be decreasing..

Answer:

83.08

Step-by-step explanation:

this means that they want only two numbers after the decimal point

if the number is up to five round it up and call it one the add it to the number before it

hope it helps

83.08 is the correct notation of 83.07718 to two decimal places.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

To write a number correctly to two decimal places, you need to look at the third decimal place digit.

If this digit is 5 or greater than 5, you will need to round up the second decimal place digit by adding 1 to it.

If this digit is less than 5, you simply leave the second decimal place digit as it is.

In the case of 83.07718, the third decimal place digit is 7, which is greater than 5. Therefore, we need to round up the second decimal place digit (7) by adding 1 to it, resulting in 83.08. This is the number written correctly in two decimal places.

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[tex]\text{Let the number be x,}\\\\~~~~~~~~x+64\leq 36\\\\\implies x \leq 36 - 64\\\\\implies x \leq -28[/tex]

Answer:

Graphs can be used to represent functions

The value of a is less than 0.

The function is given as:

The parent function of f(x) is:

So, by comparison:

The function becomes:

Next, we identify the vertex (in this case, the vertex is the minimum point on the graph)

So, we have:

Substitute these values in

So, the function becomes

From the graph, we have the following point;

So, the function becomes

Subtract 2 from both sides

Square both sides

Divide both sides by -9

So, we have:

-1 is less than 0.

Hence, the value of a is less than 0.

Step-by-step explanation:

Answer:

The value of a in this function is 0

Step-by-step explanation:

The given function is

[tex]f(x) = a(x + k)^\frac{1}{n} + c.[/tex]

Here , f(x) is y = [tex]x^{\frac{1}{2} }[/tex] So , n = 2.

By substituting the value we get the function :

[tex]f(x) = a(x + k)^\frac{1}{2} + c.[/tex]

The vertex of the graphs are : (k, c) = (-5 ,2)

The function becomes:

[tex]f(x) = a(x + 5)^\frac{1}{2} + 2[/tex]

The following point on the graph shows : (x, y) = (-4 , 5)

The function becomes:

[tex]5 = a(-4+ 5)^\frac{1}{2} + 2\\5 = a(-9)^\frac{1}{2} + 2\\\\\3 = a(-9)^{\frac{1}{2} }(Subtract 2 from both side )\\\\9 = a (-9) ( Square both sides) \\\\-1 =a ( Divide both side by -9)\\[/tex]

a = -1

Here , -1 is less than zero

Hence , the value of a is less than o.

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The formula for calculating the mark up percentage is as follows:

sticker price - invoice price/invoice price • 100 = percent mark up

Percentage mark up can be described as follows:

percentage mark up = selling price per unit - cost price per unit / cost price per unit × 100

Therefore,

Mark up is the difference between a product's selling price and cost as a percentage of the cost.

Therefore, the formula for calculating the mark up percentage is as follows:

sticker price - invoice price/invoice price • 100 = percent mark up

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Answer:

6.5 x 10^7

Step-by-step explanation:

give brainliest, please!

hope this helps :)

The arrangement of the rose plants on the triangular plot is such that they

form a series or progression that is defined.

The number of rows on Bill's plot is; 8 rows

The given parameters for the triangular plot are;

Number of plants at the corner = 1 plant

Number of additional plants per row = 6 plants

Number of rose plants = 150 rose plants

The number of rows in the plot.

The difference between successive rows, d = 6

The number rose at the top vertex, a = 1

Therefore, the rose in the garden forms an arithmetic progression

The first term, a = 1

The common difference, d = 6

The number of rows Bill's plot will have, n is given by the sum of n in terms of

an arithmetic progression, Sn, is given as follows;

[tex]S_n=\frac{n}{2}[2a+(n-1)\times d[/tex]

When Sn = 150, we get;

[tex]150=\frac{n}{2} [2\times 1+(n-1)\times 6[/tex]

150 = 3·n² - 2·n

3·n² - 2·n - 150 = 0

Taking only the positive solution for n, we have;

[tex]n_{1,\:2}=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\cdot \:3\left(-150\right)}}{2\cdot \:3}[/tex]

[tex]n_{1,\:2}=\frac{-\left(-2\right)\pm \:2\sqrt{451}}{2\cdot \:3}[/tex]

[tex]n=\frac{1+\sqrt{451}}{3},\:n=\frac{1-\sqrt{451}}{3}[/tex]

The number of rows Bill's plot has, n ≈ 7.3965

Given that the 7th row is completed, an 8th row will be present on Bill's plot

The number of rows Bill's plot will have = 8 rows

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