A circular mirror is surrounded by a square metal frame. The radius of the mirror is 3x. The side length of the metal frame is 15x. What is the area of the metal frame?

Answer:

Here is a similar question:

A bakery uses 10 1/5 ounces of icing for every 1/4 of a cake. What is the unit rate in ounces of icing per cake.

The unit rate in ounces of icing per cake = 40 4/5 ounces

Step-by-step explanation:

Given:

Ounces of ice used for every 1/4 cake = 10 1/5

We have to find the unit rate.

Let the unit rate be 'x' .

Unit rate is the rate when we use unit 'one' as our reference to find any value.

Lets convert the mixed fraction of ounces.

⇒ [tex]10\frac{1}{5} = \frac{(10\times 5)+1}{5} =\frac{51}{5}[/tex]

Portion of the cake used = [tex]\frac{1}{4}[/tex]

To find the unit rate here we must divide :

⇒ [tex]x=\frac{number\ of\ ounces\ used}{portion\ of\ the\ cake}[/tex]

⇒ [tex]x=[/tex] [tex]\frac{51}{5}[/tex]  ÷  [tex]\frac{1}{4}[/tex]

⇒ [tex]x=[/tex] [tex]\frac{51}{5}\times \frac{4}{1}[/tex]

⇒ [tex]x=[/tex] [tex]\frac{51\times 4}{5}[/tex]

⇒ [tex]x=[/tex] [tex]\frac{204}{5}[/tex]

⇒ [tex]x=[/tex] [tex]40\frac{4}{5}[/tex]  Or [tex]40.8[/tex]  

Hence, the unit rate in ounces of icing per cake = 40 4/5 ounces.

Answer:

Another similar question:

A bakery uses 10 3/5 ounces of icing for every 1/4 of a cake. What is the unit rate in ounces of icing per cake?

Step-by-step explanation:

Answer is 42 2/5

10 3/5 ÷ 1/4 = 53/5 ÷ 1/4

= 53/5 x 1/4

= 212/5

= 42 2/5

Answer:

35.0 units

Step-by-step explanation:

we know that

A mid-segment of a triangle is a segment connecting the midpoints of two sides of a triangle. This segment is always parallel to the third side, and the length of the mid-segment is half the length of the third side

so

[tex]6x+5=\frac{1}{2}(3x+55)[/tex]

solve for x

[tex]12x+10=3x+55\\12x-3x=55-10\\9x=45\\x=5[/tex]

Find the length of the mid-segment

substitute the value of x

[tex]6(5)+5=35.0\ units[/tex]

Answer: has because 1/4 is 25 and 3/4 is 75

Step-by-step explanation:

The expression for the new function (fog(x)) = x⁸ + 8x⁴

What is a composite function?

A composite function some called function of a function is a process whereby two functions produce a third function.

Let assume there is a function f(x) and g(x), a composite function fog(x) read  as f of g of x, produces a third function h(x).

In the given question, we are to find (fog) (x), we will replace the value of the function g(x) for x in f(x).

i.e.

f(g(x) = x² + 8x  

[tex]f(g(x) = (x^4)^2+8(x^4)[/tex]

[tex]f(g(x)) = x^8+8x^4[/tex]

Answer:

3

Step-by-step explanation:

-1/4 = - 0.25

-0.25 * - 12 = 3

Answer:

of wut

Step-by-step explanation:

Answer:

I believe the answer is -15, I calculated it and thats what i got

Step-by-step explanation:

Tessa's account balance is $-15.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that Tessa had $90 in her checking account. She paid her cable/internet bill for $75.She deposited $50 from her part-time job before writing a check for $80 to pay her credit card bill.

The remaining amount is calculated as:-

Balance = 90 + 50 - 75 -80

Balance = $-15

Hence, the account balance is $-15.

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Answer: 155

Step-by-step explanation: Well percent means over 100 so we can set up an equation for this problem by reading it from left to right.

What number means x, is means equals,

62% is 62/100, of means times 250.

So we have the equation  x = 62/100 · 250.

Simplifying on the right side side of the equation, notice that 62/100 reduces to 31/50 so we have x = 31/50 · 250.

Think of the 250 as 250/1.

So we can cross cancel the 250 and 50 to 50 and 1.

So we 31 times 5 over 1 or 155.

So 155 is 62% of 250.

The simplified expression is x^2 - 14xy + 49y^2.

To multiply the expression (x - 7y)^2 using the Special Product Formula, we can use the formula (a - b)^2 = a^2 - 2ab + b^2.

In this case, a = x and b = 7y. Plugging these values into the formula, we get:

(x - 7y)^2 = x^2 - 2(x)(7y) + (7y)^2

Simplifying further:

= x^2 - 14xy + 49y^2

So, the simplified expression is x^2 - 14xy + 49y^2.

The relation {(5 , 11) , (-9 , 3) , (0 , 9) , (-6 , 11)} is a function ⇒ C

Step-by-step explanation:

Let us revise the relation and the function:

A. {(11 , 5) , (3 , -9) , (11 , -6)

∵ The input 11 has two outputs 5 and -6

∵ In the function each input has only one output

∴ The relation is not a function

B. {(0 , 11) , (-9 , 3) , (0 , 9) , (-9 , -6)

∵ The inputs 0 and -9 have two outputs 11 , 9 and 3 , -6

∵ In the function each input has only one output

∴ The relation is not a function

C. {(5 , 11) , (-9 , 3) , (0 , 9) , (-6 , 11)}

∵ Each input has only one output

∵ In the function each input has only one output

∴ The relation is a function

D. {(5 , 11) , (-9 , 3) , (0 , 9) , (0 , -6)}

∵ The input 0 has two outputs 9 and -6

∵ In the function each input has only one output

∴ The relation is not a function

The relation {(5 , 11) , (-9 , 3) , (0 , 9) , (-6 , 11)} is a function

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Answer:

D

Step-by-step explanation:

Answer:

[tex]A=\pi (7)^2=153.94\ unit^2[/tex]

Step-by-step explanation:

Area of the Circle: The area of the circle of radius [tex]r[/tex] is given by [tex]\pi r^2[/tex].

[tex]Here\ r=7\\\\A=\pi (7)^2\\\\A=\pi\times 49\\\\A=49\pi\\\\A\approx 153.94\ unit^2[/tex]

Answer:

False

Step-by-step explanation:

Whichever has more heat (in this case the stove) has more thermal energy

To solve this, you need to isolate/get the variable "c" by itself in the equation:

4c + 8c = -55 + 3c    You can first combine like terms (4c and 8c)

12c = -55 + 3c         Subtract 3c on both sides

9c = -55       Divide 9 on both sides

[tex]c=-\frac{55}{9}[/tex]

Step-by-step explanation:

We have,

[tex]\dfrac{6}{7} \times 42.21[/tex]

To find, the value of [tex]\dfrac{6}{7} \times 42.21[/tex] = ?

∴ [tex]\dfrac{6}{7} \times 42.21[/tex]

= [tex]\dfrac{6}{7} \times \dfrac{4221}{100}[/tex]

We know that,

The properties of rational numbers,

[tex]\dfrac{a}{b} \times \dfrac{c}{d} =\dfrac{a\times c}{b\times d}[/tex]

= [tex]\dfrac{6\times 4221}{7\times 100}[/tex]

= [tex]\dfrac{25326}{700}[/tex]

= 36.18

Thus, the value of [tex]\dfrac{6}{7} \times 42.21[/tex]= 36.18

Answer:

No.  3/10 is NOT greater that 3/5.

Step-by-step explanation:

Take two pizzas for example.  Cut one into 10 slices and the other into 5.  Take three out of both and see which one has more of the pie gone.  

Answer:No, You can set it up as a proportion to compare.

Step-by-step explanation:

You can check by changing 3/5 into 6/10(10 is a common denominator, what u do to the bottom, you must do at the top)and as you can see, 6/10 is more than 3/10.

The variable 'a' in Albin's equation represents the number of minutes Albin was late for picking up from the daycare, with 3 dollars as the base fee and 0.50 dollars charged for each minute late.

The variable a in Albin's equation, 10.50 = 0.50a + 3, represents the number of minutes of Albin's late pick-up from the daycare. The base fee of the daycare is 3 dollars, which is a fixed amount, while 0.50 dollars is the rate charged per minute for being late. The equation is a way to calculate the total fee based on the minutes Albin is late.

For comparison, if we look at Aaron's Word Processing Service, the total cost of services would be represented by y = 31.50 + 32x, where 31.50 is a fixed cost and the cost for word processing is 32 dollars per hour (x). Similarly, for Svetlana's tutoring sessions, the total income she earns is given by y = 25 + 15x, where 25 is a one-time fee and 15 dollars per hour is her rate of earning.

Answer:

[tex]19p+2[/tex]

Step-by-step explanation:

we have

[tex]5(2p+1)+3(3p-1)[/tex]

Applying Distributive Property

[tex]5(2p)+5(1)+3(3p)+3(-1)[/tex]

[tex]10p+5+9p-3[/tex]

Combine like terms

[tex]19p+2[/tex]

Answer:

d) 15/8

Step-by-step explanation:

tgB =  AC/AB = 15/8

The tangent of an angle is the length of the opposite side (AC) divided by the length of the adjacent side (AB).

Answer:

24,000

Step-by-step explanation:

Answer:

$3.19

Step-by-step explanation:

so he starts with $18.90 and we know that he spent $2.95. So we will subtract  $2.95 from $18.90. So we are left with $15.95. But now its says he bought 5 items with $15.95. So we will divide 15.95 by 5. So the price of the item that he bought 5 of is $3.19

If you are at a higher level you can use this method:

make and equation of: 5x + 2.95 = 18.90

with this you would subtract 2.95 and then divide by 5 just like we did above.

Answer:

d. 15.95

Step-by-step explanation:

So if one item cost $2.95 and he bought 5 other items that were the same price, we first have to subtract $2.95 from the total which is $18.90.

18.90 - 2.95 = 15.95

Now, to find the cost of the other five items we divide the amount of money left by 5.

15.95 / 5 = 3.19

So each of the other five items costs $3.19.

To find the total cost of the five items together, we multiply 3.19 by 5.

3.19 x 5 = 15.95

Answer:

7/8 probability means that it is likely

Step-by-step explanation:

7/8 probability means that it is likely because 8/8 would mean certain. The closer the number gets to 8/8, the more likely it becomes. The farther away it goes, the less likely it becomes. Also, because half of 8 is 4, if the number on top is anything over 4, it means the chance is likely. If it's under 4, it's unlikely. And if it's exactly 4, then that means it is a 1/2 chance like flipping a coin.

"However, everything I just wrote only applies for this specific probability."

Answer:

Two figures are congruent if they can be superimposed so that they fit exactly. It can be shown that two plane polygons are congruent if and only if a one-to-one correspondence can be established between them such that corresponding sides have the same length and corresponding angles have the same measure.

Thus, figures that are the same size and shape are congruent. Corresponding parts of congruent figures are congruent. Congruent figures, such as those below, may be in different positions.

Congruent shapes

A figure has line symmetry if it can be folded in half and the two halves are congruent. The line made by the fold is the line of symmetry. Line symmetry is also called bilateral symmetry. Figures can have no lines of symmetry or an unlimited number of lines of symmetry.

Step-by-step explanation:

Final answer:

Symmetry refers to a balanced and proportional similarity an object exhibits across a dividing line, while congruency means two objects are identical in shape and size but may differ in position. Human bodies show bilateral symmetry, and symmetry is important for biological functionality and aesthetics. Congruency, meanwhile, is about identical geometry, regardless of orientation or position.

Explanation:

The difference between symmetry and congruency is foundational in understanding geometric principles. Symmetry refers to the balanced and proportional similarity that an object has with respect to a dividing line, plane, or center.

When an object exhibits symmetry, it means that if you were to fold it along its line of symmetry, the two halves would match up perfectly, reflecting one another. For instance, human body plans illustrate bilateral symmetry, where the body can be split into left and right halves that are mirror images of each other.

On the other hand, congruency is a concept that denotes when two shapes are identical in form and size, although they may be flipped, rotated, or moved. In geometry, when two figures are congruent, they have exactly the same dimensions and shape, but their positions may vary. A real-world example of congruence can be seen in the uniformity of manufactured products like tiles or bricks.

To observe how symmetry extends to our senses, consider that our eyes and ears are positioned symmetrically on either side of our head, providing balanced input to our brain which helps us navigate our environment effectively. This speaks to the importance of symmetry not just in aesthetics but also in biological functionality.

Answer:

52 / 27

Step-by-step explanation:

To multiply mixed numbers, convert them into improper fractions. Multiply the two improper fractions together and simplify the result.

To multiply mixed numbers, we first convert them into improper fractions. To convert 1 1/3 into an improper fraction, we multiply the whole number (1) by the denominator (3) and add the numerator (1). This gives us 4/3. Similarly, to convert 1 4/9 into an improper fraction, we multiply the whole number (1) by the denominator (9) and add the numerator (4). This gives us 13/9.

Now, we can multiply the two improper fractions together. 1 1/3 times 1 4/9 equals (4/3) * (13/9). To multiply fractions, we multiply the numerators together and multiply the denominators together. So, (4/3) * (13/9) equals (4 * 13) / (3 * 9), which simplifies to 52/27.

Therefore, 1 1/3 times 1 4/9 in fraction form is equal to 52/27.

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Answer:

the correct answer is d

Step-by-step explanation:

The Area of rectangle is 30 sq. unit.

The distance between two points A( a,b) and B(c, d) in coordinate plane is

D= √(c- a)² + (d- b)²

Given:

From the figure the coordinates of rectangle are A(3, 8), B(6, 11), C(11, 6) and D(8, 3).

Using Distance Formula

length: l = √(8-3)² + (3-8)² = √25 + 25 = √50

width: w= √(6-3)² + (11- 8)² = √9+9 = √18

So, the area of rectangle = l x w

                                          = √50 x √18

                                          = √50 x √18

                                          = √900

                                          = 30 sq. unit.

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As, the Questions figure is not given. So, this question is solved with different figure but with same method of solving.

Answer: $42.21

Step-by-step explanation:

Henry; $24.12

Gregg; $24.12 / 2= $12.06

Kasey; $ 24.12 / 4= $6.03

$24.12 + $12.06 + $6.03

The equivalent options are:

"One-sixth x + 47" ⇒ 2nd

"1 and two-thirds x + 35 minus 1 and one-half x + 12" ⇒ 3rd

"5 (one-third x) + (5) (7) minus (3) (one-half x) + (3) (4)" ⇒ 4th

Step-by-step explanation:

The expression is: 5( [tex]\frac{1}{3}[/tex] x + 7) - 3( [tex]\frac{1}{2}[/tex] x - 4) to find the equivalent to it:

Multiply the bracket ( [tex]\frac{1}{3}[/tex] x + 7) by 5

∵ 5( [tex]\frac{1}{3}[/tex] x + 7) = 5(

Multiply the bracket ( [tex]\frac{1}{2}[/tex] x - 4) by - 3

∵ -3( [tex]\frac{1}{2}[/tex] x - 4) = -3(

∴ 5( [tex]\frac{1}{3}[/tex] x + 7) - 3( [tex]\frac{1}{2}[/tex] x - 4) =  [tex]\frac{5}{3}[/tex] x + 35 -  [tex]\frac{3}{2}[/tex] x + 12

Add the like terms

∴ 5( [tex]\frac{1}{3}[/tex] x + 7) - 3( [tex]\frac{1}{2}[/tex] x - 4) = ( [tex]\frac{5}{3}[/tex] x - [tex]\frac{3}{2}[/tex] x) + (35 + 12)

To add fraction with different denominators find the LCM of the two denominators and change them by it, then divide the LCM by each denominator and multiply the quotient by the corresponding numerator

∵ LCM of 3 and 2 is 6

∵ 6 ÷ 3 = 2, then multiply 5 by 2

∴  [tex]\frac{5}{3}[/tex] = [tex]\frac{10}{6}[/tex]

∵ 6 ÷ 2 = 3, then multiply 3 by 3

∴ [tex]\frac{3}{2}[/tex] = [tex]\frac{9}{6}[/tex]

∴ ( [tex]\frac{5}{3}[/tex] x - [tex]\frac{3}{2}[/tex] x) =  [tex]\frac{10}{6}[/tex] x -  [tex]\frac{9}{6}[/tex] x = [tex]\frac{1}{6}[/tex] x

∵ 35 + 12 = 47

∴ 5( [tex]\frac{1}{3}[/tex] x + 7) - 3( [tex]\frac{1}{2}[/tex] x - 4) =  [tex]\frac{1}{6}[/tex] x + 47

The 1st option is "One-sixth x + 47"

In the step 5( [tex]\frac{1}{3}[/tex] x + 7) - 3( [tex]\frac{1}{2}[/tex] x - 4) =  [tex]\frac{5}{3}[/tex] x + 35 - [tex]\frac{3}{2}[/tex] x + 12

∵  [tex]\frac{5}{3}[/tex]  = [tex]1\frac{2}{3}[/tex]  and  [tex]\frac{3}{2}[/tex] = [tex]1\frac{1}{2}[/tex]

∴  [tex]\frac{5}{3}[/tex] x + 35 - [tex]\frac{3}{2}[/tex] x + 12 = [tex]1\frac{2}{3}[/tex] x + 35 - [tex]1\frac{1}{2}[/tex] x + 12

∴ 5( [tex]\frac{1}{3}[/tex] x + 7) - 3( [tex]\frac{1}{2}[/tex] x - 4) =  [tex]1\frac{2}{3}[/tex] x + 35 - [tex]1\frac{1}{2}[/tex] x + 12

The 2nd option is "1 and two-thirds x + 35 minus 1 and one-half x + 12"

∵ 5( [tex]\frac{1}{3}[/tex] x + 7) = 5(

∵ -3( [tex]\frac{1}{2}[/tex] x - 4) = -3(

∴ 5( [tex]\frac{1}{3}[/tex] x + 7) - 3( [tex]\frac{1}{2}[/tex] x - 4) = 5(

The 3rd option is "5 (one-third x) + (5) (7) minus (3) (one-half x) + (3) (4)"

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Answer:

[tex]5(\frac{1}{3}x)+5(7)-3 (\frac{1}{2}x)+(3)(4)[/tex]

[tex]1\frac{2}{3}x+35-1\frac{1}{2}x+ 12[/tex]

[tex]\frac{1}{6}x+47[/tex]

Step-by-step explanation:

The given expression is [tex]5(\frac{1}{3}x+7)-3 (\frac{1}{2}x- 4)[/tex]

We expand to get:

[tex]5(\frac{1}{3}x)+5(7)-3 (\frac{1}{2}x)+(3)(4)[/tex]

[tex]\frac{5}{3}x+35-\frac{3}{2}x+ 12[/tex]

As mixed number coefficients:

[tex]1\frac{2}{3}x+35-1\frac{1}{2}x+ 12[/tex]

This simplifies to:

[tex]\frac{1}{6}x+47[/tex]

Answer:

The answer is b

Step-by-step explanation:

I took the test

Answer:

B

Step-by-step explanation:

Answer: THOUSANDTHS

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

20·55/100=11

Answer: 11

Step-by-step explanation: First write 20% as a decimal by moving the decimal point 2 places to the left to get .20.

Next, the word "of" means multiply, so we have (.20)(55) which is 11.

So 11 is 20% of 55.