Pythagorus' Theroem
A rope is tied to the top of the 6m wall of a tent and tied to a peg in the ground. The peg is 2m from the bottom of the tent. How long is the rope, correct to 2d.p​

Answer:

x = 6

Step-by-step explanation:

Solve for x:

36 (x - 5) = 9 x - 18

Expand out terms of the left hand side:

36 x - 180 = 9 x - 18

Subtract 9 x from both sides:

(36 x - 9 x) - 180 = (9 x - 9 x) - 18

36 x - 9 x = 27 x:

27 x - 180 = (9 x - 9 x) - 18

9 x - 9 x = 0:

27 x - 180 = -18

Add 180 to both sides:

27 x + (180 - 180) = 180 - 18

180 - 180 = 0:

27 x = 180 - 18

180 - 18 = 162:

27 x = 162

Divide both sides of 27 x = 162 by 27:

(27 x)/27 = 162/27

27/27 = 1:

x = 162/27

The gcd of 162 and 27 is 27, so 162/27 = (27×6)/(27×1) = 27/27×6 = 6:

Answer:  x = 6

Answer:

It can be anything

Step-by-step explanation:

It just has to be grater.

The quotient of 212,960 divided by 1,000 is 212.960, achieved by moving the decimal point to the left by three places, reflecting the three zeros in 1,000.

The question asks to find the quotient when 212,960 is divided by 1,000. To find the quotient, you essentially move the decimal point three places to the left. When dividing by powers of 10, each power of 10 represents the number of places you move the decimal to the left. Therefore, 212,960 divided by 1,000 gives us 212.960. This methodology is similar to the examples provided in the reference where dividing by 10, 100, and 1000 shifts the decimal point to the left by one, two, and three places respectively.

Remember that when multiplying or dividing by powers of 10, the decimal point is moved rather than actually performing the multiplication or division action. This is one of the reasons why working with decimals and powers of 10 is simpler compared to other numbers.

Answer:

The answer is A

Step-by-step explanation:

The volume is found by [tex]l*w*h[/tex]

Therefore you multiply, 4*12*10

Answer:

The answer is A

Step-by-step explanation:

Answer:

y=3x-13/2

Step-by-step explanation:

y-y1=m(x-x1)

y-(-1/2)=3(x-2)

y+1/2=3x-6

y=3x-6-1/2

y=3x-12/2-1/2

y=3x-13/2

Answer:

1 - Avenue A is perpendicular to South St.

2 - 70°

Step-by-step explanation:

1 - North, Center, and South St. are parallel lines. Therefore Ave A will be perpendicular to the three lines.

2 - Ave B and Center street forms a 70° angle. Since Center and South St. are parallel lines, they have corresponding angles. Therefore, Ave B and South St also form a 70° angle. The same is true for Ave B and North St.

Answer:

7

Step-by-step explanation:

Let's solve your equation step-by-step.

a+6=3a−8

Step 1: Subtract 3a from both sides.

a+6−3a=3a−8−3a

−2a+6=−8

Step 2: Subtract 6 from both sides.

−2a+6−6=−8−6

−2a=−14

Step 3: Divide both sides by -2.

−2a

−2

=

−14

−2

a=7

Answer:

a=7

Answer:

-5 3/4, -5, 5/12, 1 1/5

Step-by-step explanation:

Negatives are opposite of positives when least to greatest

Answer: the first one is 3y

Step-by-step explanation:

Go to the website mathpapa , type in the problem and it gives you the answer with steps

Answer:

Length = 39 inches , breadth = 13 inches

Step-by-step explanation:

Given:

The perimeter of a rectangular atrium is 104 inches.

The length of the atrium is three times the width.

Question asked:

The length and the breadth of rectangular atrium = ?

Solution:

Let breadth of rectangular atrium = [tex]x[/tex]

Then, the length of rectangular atrium = [tex]3x[/tex]    (given)

Perimeter of rectangle = [tex]2\times(length + breadth)[/tex]

                               [tex]104 = 2\times( 3x + x )[/tex]

                               [tex]104 = 2\times 4x[/tex]

                               [tex]104 = 8x[/tex]

Dividing both side by 8

                               [tex]13 = x[/tex]

breadth of rectangular atrium = [tex]x[/tex] = 13 inches

length of rectangular atrium = [tex]3x[/tex] = [tex]3 \times13 = 39[/tex] inches

Thus, length and the breadth of rectangular atrium are 39 and 13 inches.

Answer:

The second number is 225.

Step-by-step explanation:

Consider the provided information.

Let the first number is x.

Second number

[tex]\dfrac{x}{\text{Second number}} =\dfrac{2}{3}\\\\\text{Second number}=\dfrac{3}{2}x[/tex]

Third number is:

[tex]\dfrac{\text{Second number}}{\text{Third number}} =\dfrac{5}{4}\\\\\text{Third number}=\dfrac{3}{2}x\times\dfrac{4}{5}=\dfrac{6}{5}x[/tex]

Fourth number is:

[tex]\dfrac{\text{Third number}}{\text{Fourth number}} =\dfrac{5}{6}\\\\\text{Fourth number}=\dfrac{6}{5}x\times\dfrac{6}{5}=\dfrac{36}{25}x[/tex]

The sum of 4 numbers is 771.

[tex]x+\dfrac{3}{2}x+\dfrac{6}{5}x+\dfrac{36}{25}x=771[/tex]

[tex]50x+75x+60x+72x=38550[/tex]

[tex]257x=38550\\x=150[/tex]

First number is 150.

[tex]\text{Second number}=\dfrac{3}{2}\times150=225[/tex]

Hence, the second number is 225.

The value of the second number is 165.21.

Step 1: Understand the problem.

We have four numbers whose sum is 771. The ratios between consecutive numbers are given. We need to find the value of the second number.

Step 2: Construct equations using the provided ratios.

Let the four numbers be represented as 2x, 3x, 4x, and 5x respectively (using the smallest common multiple of the ratios).

Step 3: Create an equation using the total of the numbers.

2x + 3x + 4x + 5x = 771

Step 4: Solve for x.

[tex]\(2x + 3x + 4x + 5x = 771\)[/tex]

[tex]\(14x = 771\)[/tex]

[tex]\(x = \frac{771}{14}\)[/tex]

[tex]\(x = 55.07\)[/tex]

Step 5: Find the value of the second number.

The second number is 3x.

[tex]\(3x = 3 \times 55.07 = 165.21\)[/tex]

So, the value of the second number is 165.21.

Answer:

3x+4

Step-by-step explanation:

Answer:

56.52

Step-by-step explanation:

C=3.14 * D

Answer:

12 inches by 15 inches

Step-by-step explanation:

Let

Width of the painting = x inches, then

Length of the painting [tex]=1\dfrac{1}{4}x[/tex] inches

The area of the painting:

[tex]A=\\ \\=\text{Width}\times \text{Length}=\\ \\=x\times 1\dfrac{1}{4}x=\\ \\=\dfrac{5}{4}x^2\ in^2[/tex]

Hence,

[tex]\dfrac{5}{4}x^2=180\\ \\x^2=\dfrac{4}{5}\times 180=4\times 36=144\\ \\x=12\ inches\\ \\\text{Width}=12\ inches\\ \\\text{Length}=\dfrac{5}{4}\times 12=15\ inches[/tex]

Answer: 7%

Step-by-step explanation:

Answer:

2i

Step-by-step explanation:

The square root of -4 is equal to 2i.

The square root of -4 can be simplified using the imaginary number i. Since the square root of a negative number is not defined in the set of real numbers, we use i to express it, where i is defined as the square root of -1. Thus, the square root of -4 is calculated as follows:
√-4 = √(-1*4)
= √(-1) * √(4)
= i * 2
= 2i

This result shows that 2i is the simplified form of the square root of -4 using the imaginary number i.

volume of the speaker= 22 cubic inches

Step-by-step explanation:

Answer:

5 weeks

Step-by-step explanation:

Answer:

x = 5/4 or 1.25.

Step-by-step explanation:

10x + 4 = 6x + 9

10x - 6x = 9 - 4

4x = 5

x = 5/4.

Answer: x = 5/4 or 1.25 or 1 1/4

Step-by-step explanation:

Step 1: Subtract 6x from both sides.

10x+4−6x=6x+9−6x

4x+4=9

Step 2: Subtract 4 from both sides.

4x+4−4=9−4

4x=5

Step 3: Divide both sides by 4.

4x/4 = 5/4

The total cost of the sweater will be $36.75.

Percentage is a number or ratio which is a fraction of hundred.

Given,

Cost price of sweater =$35.

Sales tax= 5%.

The total cost of the sweater can be calculated as,

Total cost price = CP of sweater + sales tax

                          = 35 + (5/35)*100

                          =$36.75

Hence, The total cost price of sweater would be $36.75.

Learn about Percentages:

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Answer:

∠1 ≅ ∠2

Step-by-step explanation:

As shown in the figure:

We need to prove e ∥ f using the congruent angle.

So, check the options:

A) ∠2 ≅ ∠4 ⇒ (Wrong)

B) ∠1 ≅ ∠2 ⇒ (True) because a ∥ b (Given)

C) ∠2 ≅ ∠3 ⇒ It is required to prove that to prove e ∥ f , it can't be used.

D) ∠1 ≅ ∠4 ⇒  (Wrong)

The complete sentence will be:

We see that ∠1 ≅ ∠2 by the alternate exterior angles theorem.

Therefore, angle 2 is congruent to angle 3 by the transitive property.

The missing information in the paragraph proof is: ∠2 ≅ ∠4.

In the given proof, it is correctly established that angle 1 is congruent to angle 3 because lines a and b are parallel, and this is due to the alternate exterior angles theorem.

Furthermore, it is correctly deduced that angle 2 is congruent to angle 3 through the transitive property.

However, to conclude that lines e and f are parallel using the converse alternate exterior angles theorem, it is essential to establish that angle 2 is congruent to angle 4.

Without this information, the proof is incomplete because it doesn't demonstrate the congruence between the corresponding angles on lines e and f at their intersection with line b.

To complete the proof, you would need to show that ∠2 ≅ ∠4, thereby demonstrating that all pairs of corresponding angles between lines e and f are congruent.

This additional congruence statement would justify the application of the converse alternate exterior angles theorem, allowing you to conclude that e ∥ f.

for such more questions on angle

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Answer:

a.  [tex]$ \frac{\textbf{17}}{\textbf{4}} $[/tex]

b.  [tex]$ \frac{\textbf{3}}{\textbf{8}} $[/tex]

Step-by-step explanation:

a. [tex]$ \textbf{3} \hspace{1mm} \textbf{+} \hspace{1mm} \textbf{1}\frac{\textbf{1}}{\textbf{4}} $[/tex]

A mixed fraction of the form [tex]$ a\frac{x}{y} = a + \frac{x}{y} $[/tex]

[tex]$ \therefore 3 + 1\frac{1}{4} = 3 + 1 + \frac{1}{4} $[/tex]

[tex]$ = 4 + \frac{1}{4} $[/tex]

[tex]$ = \frac{\textbf{17}}{\textbf{4}} $[/tex]

b. [tex]$ \textbf{2} \hspace{1mm} \textbf{-} \hspace{1mm} \textbf{1}\frac{\textbf{5}}{\textbf{8}} $[/tex]

A mixed fraction of the form [tex]$ -c\frac{a}{b} = - c - \frac{a}{b} $[/tex]

[tex]$ \therefore 2 - 1\frac{5}{8} = 2 - 1 - \frac{5}{8} $[/tex]

[tex]$ = 1 - \frac{5}{8} $[/tex]

[tex]$ = \frac{8 - 5}{8} $[/tex]

[tex]$ = \frac{\textbf{3}}{\textbf{8}} $[/tex]

Hence, the answer.

Answer:

17 pies and one half pie

Step-by-step explanation:

Answer:

12x+60

Step-by-step explanation:

12 gets multiplied with x

12 gets multiplied with 5

Which gives 12x + 60

Answer:

The equation is

(x+27)= 58

Therefore the customer purchased 31 bananas

Step-by-step explanation:

Given , A customer at the grocery store purchased 27 apple and unknown number of bananas. The customer purchased a total of 58 apple and bananas.

Let the number bananas be x

He purchased a total (x+27)  apples and bananas.

According to the problem,

(x+27)= 58

⇔x= 58-27

⇔x = 31

Therefore the customer purchased 31 bananas

Answer:

6 days

Step-by-step explanation:

Data given:

Vancouver is in the British Columbia

3/5 of the vacation was spent in British Columbia

1/2 of the time spent in British Columbia was spent in Vancouver.

The whole vacation was 20 days long

total days spent in British Columbia = 3/5 *20

total days spent in British Columbia = 12

Since the 1/2 of the time in British Columbia was spent in Vancouver then

time spent in Vancouver = 1/2 * 12

time spent in Vancouver =6 days

Mara spent [tex]\(\frac{3}{10}\)[/tex] of her vacation in Vancouver. If her vacation lasted 20 days, she spent 6 days in Vancouver.

 Mara spent [tex]\(\frac{3}{10}\)[/tex]of her vacation in British Columbia. While in British Columbia, she spent [tex]\(\frac{1}{2}\)[/tex] of her time in Vancouver.

To find the fraction of her entire vacation that Mara spent in Vancouver, we multiply the two fractions:

[tex]\[ \text{Fraction of vacation in Vancouver} = \frac{3}{5} \times \frac{1}{2} = \frac{3 \times 1}{5 \times 2} = \frac{3}{10} \][/tex]

So, Mara spent [tex]\(\frac{3}{10}\)[/tex] of her vacation in Vancouver.

Next, to find out how many days she spent in Vancouver, we take the total number of days of her vacation, which is 20 days, and multiply it by the fraction of the vacation spent in Vancouver:

[tex]\[ \text{Days in Vancouver} = 20 \times \frac{3}{10} \][/tex]

[tex]\[ \text{Days in Vancouver} = 6 \][/tex]

 Therefore, Mara spent 6 days in Vancouver.

Name the property the equation illustrates

(ab)3 = a(b3)

A. Commutative property of addition

B. Associative property of Multiplication

C. Associative Property of Addition

D. Inverse Property of Multiplication

Associative property of Multiplication

From given equation

(ab)3 = a(b3)

We have to find the property used here

We find the brackets are interchanged

So here, given is a multiplication equation

Therefore, Associative property of Multiplication  is used

This property says that when we are multiplying it does not matter where you put the parenthesis

The result will be same wherever we put the parenthesis in multiplying two or more numbers

Which means,

[tex]a \times (b \times c) = (a \times b) \times c[/tex]

Therefore, from given,

[tex]a \times (b \times 3) = (a \times b) \times 3[/tex]

Thus associative property of multiplication is used

Answer:

(x - 4, y + 3)

Step-by-step explanation:

This is because when you follow the movement of the individual points you can see that they have moved 3 spaces up which is shown as y + 3, and they have moved 4 spaces to the left which is shown as x - 4

Answer:

The correct answer is: D

Step-by-step explanation:

(x - 4, y + 3)

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Answer:

(-9,-9)

I Agree

Step-by-step explanation: