Consider the enlargement of a triangle that has a scale factor of 7.5.
A small triangle has a base of 5 centimeters and height of 2 centimeters. A larger triangle has a base of b and height of a.
Area Original = 1
2
(5)(2) = 5 cm2
What is the area of the enlarged triangle? cm2

To find the area of the orange band, subtract the area of the yellow square from the area of the larger square.

To find the area of the orange band, we need to subtract the area of the yellow square from the area of the larger square. The side length of the larger square is 8 inches because it is twice the side length of the yellow square, which is x inches. So, the area of the larger square is 8 * 8 = 64 square inches. The area of the yellow square is x * x = x^2 square inches. Therefore, the area of the orange band is 64 - x^2 square inches.

Final answer:

To calculate the area of the orange band, find the area of the larger square using the side length of x + 22 inches and subtract the area of the smaller yellow square with side length x. The expression for the area of the orange band is [tex](x + 22)^2 - x^2[/tex], which simplifies to 44x + 484 square inches.

Explanation:

To calculate the area of the orange band, you need to determine the area of the outer (larger) square and subtract the area of the inner (smaller) yellow square. First, find the side length of the larger square, which is the side length of the yellow square plus twice the width of the orange band, so it's x + 2(11) inches. Thus, the side length of the larger square is x + 22 inches.

Now, calculate the area of both squares. The area of the larger square is [tex](x + 22)^2[/tex] square inches, and the area of the yellow square is [tex]x^2[/tex] square inches. The area of the orange band is the difference between these two areas:

Area of the larger square:[tex](x + 22)^2[/tex]

Area of the yellow square: [tex]x^2[/tex]

Area of the orange band: [tex](x + 22)^2 - x^2[/tex]

To find the area of the orange band, you expand the expression [tex](x + 22)^2[/tex], which gives you [tex]x^2 + 44x + 484[/tex], then subtract the area of the yellow square [tex]x^2[/tex], resulting in 44x + 484 square inches, which is the area of the orange band.

It would take 6.99 kilometers of thread to make 9 boxes of shirts.

Step-by-step explanation:

Step 1; First we convert the mixed fractions into improper fractions. So

2[tex]\frac{1}{5}[/tex] becomes [tex]\frac{11}{5}[/tex] after multiplying 2 with 5 and adding 1 while 5 remains.

2[tex]\frac{5}{6}[/tex] becomes [tex]\frac{17}{6}[/tex] after multiplying the 2 with 6 and adding 5 while 6 remains.

Step 2; Next we equate the given data; [tex]\frac{11}{5}[/tex] kilometers of thread = [tex]\frac{17}{6}[/tex] boxes of thread. We must make the RHS equal to 1 to find out the kilometers of thread needed to make 1 box of shirts. So we multiply [tex]\frac{6}{17}[/tex] on both sides to make the RHS equal to 1.

[tex]\frac{11}{5}[/tex] × [tex]\frac{6}{17}[/tex] = [tex]\frac{17}{6}[/tex]× [tex]\frac{6}{17}[/tex]= 1, So [tex]\frac{11}{5}[/tex] × [tex]\frac{6}{17}[/tex] = [tex]\frac{66}{85}[/tex] km of thread. So [tex]\frac{66}{85}[/tex] kilometers of the thread is required to make 1 box of shirts so we multiply this with 9 to see thread required to make 9 boxes of shirts.

Thread required for 9 boxes of shirts = [tex]\frac{66}{85}[/tex] × 9= [tex]\frac{594}{85}[/tex] = 6.9882 kilometers of thread. This is rounded off to 6.99 kilometers of thread.

Answer:

Boden's conjecture is correct

Step-by-step explanation:

we know that

If two angles are complementary, the cofunction identities state that the sine of one equals the cosine of the other and vice versa.

A right triangle, has two acute angles.

The two acute angles are complementary

so

In any right triangle, the sine of one acute angle is equal to the cosine of the other acute angle

therefore

Boden's conjecture is correct

Answer:

Yes, because the leg opposite one of the acute angles is adjacent to the other acute angle

Step-by-step explanation:

Answer:

D.30,15,14

Step-by-step explanation:

Answer:

  3.25 +7.25m

Step-by-step explanation:

The cost of membership in Jump Rope Gym can be modeled by ...

  total cost = initial fee + m × (monthly fee)

  j = 6.50 +17.50m

Likewise, the cost for Run Run Run Gym is ...

  r = 9.75 +24.75m

Then the savings by joining the Jump Rope Gym is ...

  r -j = (9.75 +24.75m) -(6.50 +17.50m) = 3.25 -7.25m . . . .savings

Step-by-step explanation:

[tex]9x {}^{2} + 4x - 30x - 6[/tex]

[tex]9 {x}^{2} - 26x - 6[/tex]

Answer: 9x-5

Step-by-step explanation:

Combine like terms

Answer: he is right the answer is -2

Step-by-step explanation:

The common difference (d) is -2.

In an arithmetic sequence, the common difference (d) is the constant value by which each term differs from the previous term.

To find the common difference in the sequence 100, 98, 96, 94, 92..., we can observe the difference between consecutive terms:

98 - 100 = -2

96 - 98 = -2

94 - 96 = -2

92 - 94 = -2

We see that each term is decreasing by 2. Therefore, the common difference (d) is -2.

Answer: 25 by 50 ft

Hope this helps

The dimensions of the rectangle will allow for the most economical fence to be built are 30 feet by 15 feet

Given that, rectangular area=450 square feet.

The formula to find the area of a rectangle is Area=Length×Breadth.

Let the length of the rectangle be x and the breadth of the rectangle be y.

Now, 450=xy.

x=450/y

The cost of three sides is $3 per foot.

That is, 3x+3x+3y

The cost on the fourth side is $9 per foot.

That is, 9y

Total cost=6x+12y

Now, Total cost=6×450/y+18y

Let the minimum cost be 0.

2700/y+12y=0

⇒2700/y²-12=0

⇒12y²=2700

⇒y=15 feet

So, 450/15=x=30 feet.

Therefore, the dimensions of the rectangle are 30 feet by 15 feet.

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Explanation:

Focus only on the diamond cards. There are 13 of them total. Out of the 13 diamond cards, there is one king of diamonds. So the probability of getting a king, if we know 100% the card is a diamond, is 1/13.

---------------

You can use a slightly longer method through a conditional probability

A = card is a king

B = card is a diamond

P(A and B) = probability of king and diamonds = 1/52

P(A \ B) = probability of event A happens given we know B happens

P(A \ B) = P(A and B)/P(B)

P(A \ B) = (1/52)/(13/52)

P(A \ B) = (1/52) ÷ (13/52)

P(A \ B) = (1/52) * (52/13)

P(A \ B) = 1/13

The probability that the card is a King is 1/13

Probability is the likelihood or chance that an event will occur.

Probability = Expected outcome/Total outcome

Given that a card is drawn at random from a pack of 52 playing cards, the total outcome is 52

If the card is a king, the expected outcome is 4

Pr(selecting a king) = 4/52 = 1/13

Hence the probability that the card is a King is 1/13

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Answer:

2x

Step-by-step explanation:

x and 2 are common to both 10x and 22x, so 10x + 22x = 2x(5 + 11)

The GCF is 2x.

Answer:

x = 10

Step-by-step explanation:

Given

4x + 2 = 42 ( subtract 2 from both sides )

4x = 40 ( divide both sides by 4 )

x = 10

Answer:

Step-by-step explanation:

4x+2=42

4x=42-2

4x=40

x=40/4

X=10

Answer:

First term: A(1) = 5

Fourth term: A(4) = 5 1/2

Tenth term: A (10) = 6 1/2

Step-by-step explanation:

Let's find the first, fourth and tenth terms of the arithmetic sequence described by the given rule:

A(n) = 5 + (n-1) (1/6)

First term:

A(1) = 5 + (1-1) (1/6)

A(1) = 5 + (0) (1/6)

A(1) = 5

Fourth term:

A(4) = 5 + (4-1) (1/6)

A(4) = 5 + (3) (1/6)

A(4) = 5 + 3/6 = 5 3/6 = 5 1/2 (simplifying)

Tenth term

A(10) = 5 + (10-1) (1/6)

A(10) = 5 + (9) (1/6)

A (10) = 5 + 9/6 = 6 3/6 = 6 1/2 (simplifying)

Answer: Perimeter = 2(L + W) and

as a simplified expression is, 8x + 2

Step-by-step explanation: The length is represented by L and the width is represented by W in the expression above.

However, since we have been given the sides of the rectangle as x + 2 and 3x - 1, we shall substitute for the values of these in the expression representing the perimeter.

2(L + W) can now be written as

2( {x + 2} + {3x - 1} )

2(x + 2 + 3x - 1)

By collecting like terms, we now have

2(4x + 1)

8x + 2.

The expression can now be simplified as 8x + 2

Answer: mikey ate more

Step-by-step explanation: mick ate 2/5 which is 4 out of ten mikey ate half which is 5 out of 10 so mikey ate more

brainliest plz

Final answer:

Mikey the monkey ate more bananas than Mick, consuming 5 compared to Mick's 4 bananas.

Explanation:

Let's calculate how many bananas each monkey ate. We'll start with Mick the monkey, who had 10 bananas and ate two fifths of them.

Calculate two fifths of 10 bananas: (2/5) × 10 = 4 bananas.

Mick therefore ate 4 bananas.

Now, let's calculate for Mikey the monkey, who also had 10 bananas and ate half of them.

Calculate half of 10 bananas: (1/2) × 10 = 5 bananas.

Mikey ate 5 bananas.

Mikey the monkey ate more bananas than Mick because 5 is greater than 4.

Answer:

Decimal form: 21.25

Mixed number: 21 1/4

Exact form: 85/4

Answer:

Step-by-step explanation:

3x1=3

2x3=6

2+1=3

3+3=6

Two equations that have the solution (3,6) include y = 2x and x + y = 9, satisfying the point when their values are substituted.

To write two equations that would have the solution of (3,6), we need to construct linear equations where the point (3,6) satisfies both equations. Here are two examples that fit the criteria:

The first equation could be y = 2x, because when x=3, then y=2(3)=6.

The second equation could be x + y = 9, because when x=3 and y=6, then 3 + 6 = 9.

These two examples clearly have the solution (3,6) when the respective values for x and y are substituted.

Answer:74

Step-by-step explanation:

Answer:

5 7/12

Step-by-step explanation:

7/4 + 1/6 +x = 15/2

Lowest Common denominator =12

21/12 + 2/12 + x = 90/12

23/12 +x= 90/12

x= 90-23 = 67/12 = 5 7/12

The answer for 36/4 + 11 [tex]\times[/tex] 8 = 97.

Step-by-step explanation:

The order of operation is done by using BODMAS rule.

B - bracket

O - of

D - division

M - multiplication

A - addition

S - subtraction

step 1 :

36 divided 4 + 11 [tex]\times[/tex] 8

step 2 :

9 + 11 [tex]\times[/tex] 8

step 3 :

9 + 88

∴ The answer for 36divided4+11x8 is 97.

Answer: y=3x+4.50

Step-by-step explanation:

Answer:

4.50- 10.50/ 3x

6/3x= 2

Answer:

a) 31c + 19m ≤ 706

b) 7500c + 4300m > 84000

Step-by-step explanation:

hope it helps :p

Answer:

make sure variables are capital!

Step-by-step explanation:

Answer:

4 4/9

Step-by-step explanation:

2 1/5 X 2 2/9

= 11/5 * 20/9

= 11/1 * 4/9

= 44/9

= 4 4/9

Answer:

no

...

...

...

....

shajajs

Answer:

NO

A= 1/2 x B x H

P= A+B+C

Step-by-step explanation:

ex: triangle side 13, 6,8.5

high: 8

A= 52

P= 27.5

Answer:

$365.00

Step-by-step explanation:

4 years times 12 months equals 48 months.

$17520.00 / 48=$365.00

Answer:

Option D.

Step-by-step explanation:

        A = 1/2 (base × perpendicular height)

       A = 1/2 (x.x)

           =1/2 (x²)

      32 = 1/2 (x²)

     Multiplying both sides by 2 gives:

     32×2 = x²

     64  = x²

       8   = x

To find the third side, we use the Pythagoras theorem:

    C² = A² + B²

         = 8² + 8²

         = 128

   C = √128

       = 8√2

However, the answer will not be exact, so we  multiply the length of the base and height by 2. This gives x = 16 (Length of base = length of height)

Repeating the steps above gives C = √ (16)² + (16)²

                                                           = √256

This corresponds to option D.

The amount of tip is $6

Step-by-step explanation:

So let cost of meal be 20 x and the tip be 3 x.

⇒ 3x + 20x = 46

⇒ 23x = 46

⇒ x = 2

⇒ 3x = 3 × 2 = $6

Answer:

y or f(x), depends on the context.

Step-by-step explanation:

When graphing a function, we input a value, x, and output a value, y. This is why we have a coordinate plane.

For example, if we have y = 2x and x=2, our input, then y = 4, our output.

However, if written in function notation, f(x) = 2x, our output will still be 4, except that our output is f(x)

Answer:

f(x)

Step-by-step explanation:

Answer:

B-false

Step-by-step explanation:

It is false because where the 2 is, has to be 3, other wise it won't make sense. Because it will not equal the same thing.

Final answer:

The expression 3a + 3b is not equivalent to 3(a + 2b). The first results in 3a + 3b, while applying the distributive property to the second expression gives 3a + 6b, clearly showing the expressions are different.

Explanation:

The statement 3a + 3b is equivalent to 3(a + 2b) is false. To show this, we can apply the distributive property of multiplication over addition, which states that for any real numbers a, b, and c, a · (b + c) = a·b + a·c. Using this property, we can expand 3(a + 2b) to get 3·a + 3·2b, which simplifies to 3a + 6b. This is not the same as 3a + 3b since 3b is not equal to 6b. Therefore, the expressions are not equivalent.

Answer:

The price of a drink = $4

The price of a bag of popcorn = $5.5

Step-by-step explanation:

Let p represent popcorn and d represent drink

Harper bought 10 bags of popcorn and 6 drinks and paid $79 ➡ 10p + 6d = $79

Damian bought 3 bags of popcorn and 5 drinks and paid $36.50 ➡ 3p + 5d = $36.50

Now multiply first equation by -3 and second equation by 10

-3 × (10p + 6d) = $79 ➡ -30p - 18d = -$237

10 × (3p + 5d) = $36.50 ➡ 30p + 50d = $365

Now add the new equationd

30p + 50d -30p - 18d = $365 - $237 (-30p will eliminate 30p)

32d = $128 divide both sides of the equation by 32

32 ÷ 32d = 32 ÷ $128 ➡ d = 4

If d = 4 that means a drink costs $4 we can use this information to find the price of a bag of popcorn

3p + 5d = $36.50 (replace d with 4)

3p + 4×5 = $36.50

3p + 20 = $36.50

3p = $36.50 - 20

3p = 16.50 divide both sides by 3

p = $5.5

The question asked to set up a system of equations to determine the price of each bag of popcorn and each drink. Using the variables x and y to represent the price of popcorn and drinks respectively, the system of equations based on the information given is 10x + 6y = $79 and 3x + 5y = $36.50.

To solve this problem, we need to setup a series of equations based on the information given. Let's say:

According to the first scenario with Harper, we get:

10x + 6y = $79

From Damian's shopping, we have:

3x + 5y = $36.50

This gives us the system of equations which can be used to find individual prices of a bag of popcorn and a drink.

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