Consider a circle with a diameter of 5 centimeters. Which equation shows how the relationship between the circumference and the diameter of this circle is equivalent to π?
A) π = 5C
B) π =
5
C
C) π =
C
5
D) π =
1
5C

Answer:

.199 or 20% (.20)

Step-by-step explanation:

Percentage change:

p=(85-105)/105=-20/105=-19.047%

Rounded value: -19.05%

The minus sign indicates a decrease in amount spent.

Answer:

8. D 269.6

9. A 20 +10h

Step-by-step explanation:

8.  The large rectangle is 4+6.4+4+6.4 = 20.8 width and 10.5 length.  The area is

A = l*w = 20.8* 10.5 =218.4

The top rectangle is 6.4 width and length is 4

A = l*w =6.4*4 =25.6

The same is true for the rectangle on the bottom.

Add the three rectangles together to get the total surface area

218.4+25.6+25.6 =269.6

9. The plant is 20 inches tall

It grows 2h inches a week for 4 weeks

20 +2h*4

20 +8h

It grows h inches a week after  4 weeks

At 6 weeks, that is 2 weeks of growth

The growth is h *2

Add that to the previous total

20 +8h +2h

20 +10h

Answer:

Here's our equation:

480 * 1/3 - 60 = []

The 1/3 comes from 1 - 2/3 = 1/3 for note, as that's how much of her money is left after the fan's purchased. (if you're unsure, you can multiply 480 and 2/3 together, and then subtract that amount from 480, and you'll see you end up with the same answer as below)

The order of operations means we deal with the 480 * 1/3 first.

480 * 1/3 → 480/3 = 160

Next is subtraction:

160 - 60 = 100

So Mrs. Ricci has $100 left.

Step-by-step explanation:

Answer:

(- 8, - 4 )

Step-by-step explanation:

Under a counterclockwise rotation about the origin of 90°

a point (x, y ) → (- y, x ), thus

(- 4, 8 ) → (- 8, - 4 )

Answer:

B) III only, it doesn't suggests relationship between x and y.

Answer:

0.155

Step-by-step explanation:

Answer:

$0.15 per ounce

Step-by-step explanation:

2.48/16 = 0.155

minimum value of the quadratic function f(x) = x² - 2x + 7 is at x=1 & is (1, 6).

Step-by-step explanation:

Here we have ,  f(x) = x² - 2x + 7 or [tex]f(x) = x^2 - 2x + 7[/tex] . We need to find the minimum value of f(x) for which we need to differentiate it one time and equate it to zero . Value of x at which first differentiation of f(x) is zero will be the minimum value of function  . Let's solve this:

[tex]f(x) = x^2 - 2x + 7[/tex]

⇒ [tex]f(x) = x^2 - 2x + 7[/tex]

⇒ [tex]\frac{df(x)}{dx} = \frac{d(x^2 - 2x + 7)}{dx}[/tex]

⇒ [tex]\frac{df(x)}{dx} = \frac{d(x^2)}{dx} - \frac{d(2x)}{dx} + \frac{d(7)}{dx}[/tex]

⇒ [tex]\frac{df(x)}{dx} = 2x-2 = 0[/tex]

⇒ [tex]2x-2 = 0[/tex]

⇒ [tex]x =1[/tex]

Now, value of function at x=1 is :

[tex]f(x) = x^2 - 2x + 7[/tex]

⇒ [tex]f(x) = x^2 - 2x + 7[/tex]

⇒ [tex]f(1) = 1^2 - 2(1) + 7[/tex]

⇒ [tex]f(1) = 8- 2[/tex]

⇒ [tex]f(1) = 6[/tex]

Therefore, minimum value of the quadratic function f(x) = x² - 2x + 7 is at x=1 & is (1, 6).

The minimum value of the quadratic function f(x) = x² - 2x + 7 is 6, which occurs at x = 1, as determined by finding the vertex of the parabola.

The minimum value of the quadratic function f(x) = x² - 2x + 7 can be determined by finding the vertex of the parabola represented by the function. This is because the graph of a quadratic function is a parabola, and if the coefficient of the x² term is positive, the parabola opens upwards and the vertex represents the minimum point.

To find the vertex, use the formula -b/2a to determine the x-coordinate of the vertex. For the function f(x), the value of 'a' is 1 and 'b' is -2. Substituting these values gives us the x-coordinate of the vertex as x = -(-2)/(2*1) = 1. Substituting x = 1 back into the function f(x), we get the y-coordinate of the vertex, which is the minimum value of the function: f(1) = (1)² - 2*(1) + 7 = 6.

Therefore, the minimum value of the quadratic function f(x) is 6, occurring at x = 1.

Answer:

1800ft tall

Step-by-step explanation:

Answer:

24,48,72,96

Step-by-step explanation:

Multiples of 8

8, 16,24,32,40,48,56,64,72,80,88,96

Multiples of 12

12,24,36,48,60,72,84,96

Common multiples

24,48,72,96

Answer:

See below.

Step-by-step explanation:

"List all the multiples of 8 that are less than or equal to 100."

0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96

"List all the multiples of 12 that are less than or equal to 100."

0, 12, 24, 36, 48, 60, 72, 84, 96

Common multiples: 0, 24, 48, 72, 96

The question is about calculating a tip which is 25% of a meal cost of $12.00. The tip is calculated by multiplying the total cost of the meal by the tip percentage, converted into decimal form. The answer is $3.00.

Percentage is a mathematical concept used to express a portion of a whole as a fraction of 100. It is a versatile tool in various fields, including finance, statistics, and everyday calculations. To calculate a percentage, you divide a part by the whole and then multiply by 100. Percentages are commonly used to represent proportions, express changes, and compare values, making them vital for analyzing data, understanding discounts, and determining growth rates. In essence, percentages simplify the representation of relative quantities and are fundamental in both practical and academic mathematics.

The subject of the question is Mathematics, specifically Percentage. The student is being asked to calculate 25% of $12.00, which is the cost of Eliza's meal. To calculate the tip, multiply the total meal cost by the percentage of the tip. Here's how we can do it:

So the tip Eliza left for the waiter was $3.00.

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Answer:

23/4

Step-by-step explanation:

multiply the whole number (5) by the denominator (4) and add your numerator (3), which for you is 23, then put that over your denominator (4). so it would be 23/4 :)

Well I'm a bit confused since 5 3/4 is a mixed number. Please elaborate!

Answer:

They paid $4.00 per ticket

Step-by-step explanation:

Step 1:  Convert words into an inequality

A family buys 6 tickets to a show. They also pay $3 parking fee. They spend $27 to see the show.

6t + 3 = 27

Step 2:  Solve for t/tickets

6t + 3 = 27

6t + 3 - 3 = 27 - 3

6t / 6 = 24 / 6

t = 4

Answer:  They paid $4.00 per ticket

Answer:

4

Step-by-step explanation:

3 - 27 = 24

24 ÷ 6 = 4

4 · 6 = 24

3 + 24 = 27

A = $27

Answer:

The last one

Step-by-step explanation:

volume is v= [tex]\pi r^{2} h[/tex] . this means volume is mathematical number pi, times the (radius squared), times the height. the radius is marked at the yellow line, and the height on the side. this means you would have v = [tex]\pi[/tex][tex](x+2)^{2}[/tex][tex](3x+8)[/tex]

first, lets work out [tex](x+2)^{2}[/tex]. we can rewrite this as (x+2)(x+2). we are going to use a system called FOIL. this stands for First Outside Inside Last. This means we are going to take the first number from both and multiply them together, then the outside, inside, and last. so, for first, we will multiply x and x and then we have [tex]x^{2}[/tex], for outside we multiply x and 2 and we get [tex]2x[/tex], for inside we multiply 2 and x and we get [tex]2x[/tex], and for last we multiply 2 and 2 and we get [tex]4[/tex]. then we add all these together. [tex]x^{2} + 2x + 2x + 4[/tex]. then simplify like terms to get

[tex]x^{2} + 4x + 4[/tex]. now, we can't forget about our times [tex]\pi[/tex] and (3x+8)

this means we have to multiply [tex]x^{2} + 4x + 4[/tex] by those two.

it would look like this: ([tex]x^{2} + 4x + 4[/tex])(3x+8)[tex]\pi[/tex]

so now we are going to multiply the other two sets of parentheses

we multiply each number from the first set to each number in the second set.

The area of the triangle is 90 m²

Explanation:

Given that the base of the triangle is 15 m

The altitude of the triangle is 12 m

Area of the triangle:

The area of the triangle can be determined using the formula,

[tex]Area=\frac{1}{2}bh[/tex]

where b is the base and h is the altitude

Thus, we have,

[tex]b=15[/tex] and [tex]h=12[/tex]

Substituting the values in the above formula, we get,

[tex]Area=\frac{1}{2}(15)(12)[/tex]

Multiplying the terms, we get,

[tex]Area=\frac{180}{2}[/tex]

Dividing, we get,

[tex]Area=90 \ m^2[/tex]

Therefore, the area of the triangle is 90 m²

Answer: The Answer is 100, sorry that you got it so late.

Step-by-step explanation:

What I did

1. Find the difference between the numbers

2. Look through answer choices

3. Because the difference of 80 and 75 was 5, 105 would be 100.

Sorry if this doesn't make sense.

Answer:

0+7-4=3

Step-by-step explanation:

They started with none, hence the 0. "Gained" typically means addition, so you add seven. "Lost" is a signal word for subtraction, so subtract zero. It comes out to 4.

Answer:

6/8

Step-by-step explanation:

3/4 = 6/8 = 9/12 and so on

Answer:

9/12

Step-by-step e

Answer:

[tex]QP=20\ units[/tex]

Step-by-step explanation:

The picture of the question in the attached figure

Let

O ---> the center of the circle

we have that

Line segment QP is tangent to the circle

That means

OQ (radius) is perpendicular to segment QP

OQP is a right triangle

Applying Pythagorean Theorem

[tex]OP^2=OQ^2+QP^2[/tex]

we have

The radius is equal to

[tex]r=24/2=12\ units[/tex] ----> the radius is half the diameter

[tex]OP=r+NP=12+11.5=23.5\ units[/tex]

[tex]OQ=r=12\ units[/tex]

substitute

[tex]23.5^2=12^2+QP^2[/tex]

[tex]QP^2=23.5^2-12^2[/tex]

[tex]QP^2=408.25[/tex]

[tex]QP=20\ units[/tex]

Answer:20 units

Step-by-step explanation:

Answer:

9450 m³

Step-by-step explanation:

(S1/S2)³ = V1/V2

3³ = V1/350

New Volume = 27 × 350

= 9450 m³

To prove ABCD is a rhombus, showing that all sides of parallelogram ABCD are equal in length would suffice.

If ABCD is a parallelogram, to prove that it is a rhombus, a statement that would suffice is that all four sides of the parallelogram are of equal length.

This is because a rhombus is defined as a parallelogram with four congruent sides. If any one of its diagonals bisects an angle of the parallelogram, or its diagonals are perpendicular, or its diagonals are of the same length, these conditions would not exclusively prove it to be a rhombus, although they are properties of a rhombus. However, the definition of a rhombus centers on the equality of all sides.

Equal adjacent angles would not necessarily mean that all sides are equal, which is a requirement for a rhombus.

The correct option is (B).

To prove that a parallelogram is a rhombus, you need to show that all four sides are of equal length. A parallelogram has opposite sides that are equal and parallel, but for it to be a rhombus, every side must be equal in length to every other side.

The statement options you might have in your image could be something like:

a. Diagonals are perpendicular (AC ⊥ BD)

b. Adjacent angles are equal (∠ABC ≅ ∠CDA)

c. One pair of opposite sides are equal (AB ≅ CD)

d. Diagonals are equal (AC ≅ BD)

From these options:

- Option a: If the diagonals are perpendicular, it's an indication that the parallelogram could be a rhombus, but it's not conclusive proof because a rectangle also has perpendicular diagonals.

- Option b: Equal adjacent angles would not necessarily mean that all sides are equal, which is a requirement for a rhombus.

- Option c: Having one pair of opposite sides that are equal is already a property of a parallelogram and does not prove it's a rhombus.

- Option d: Equal diagonals would be a property of a rectangle, not necessarily a rhombus.

The conclusive proof that a parallelogram is a rhombus would be if you can show that all sides are of equal length (not provided in the typical options above), or if the diagonals are perpendicular and bisect each other into equal segments. This latter property is unique to a rhombus among parallelograms. If this were one of the choices, it would be the correct answer.

Since I can't see the options, please review them and look for the one that indicates all four sides are of equal length or that the diagonals bisect each other into equal segments and are perpendicular. That would be the correct choice to prove the parallelogram is a rhombus.

Answer:

Yes.

Step-by-step explanation:

Note that  15^2 = 122^ + 9^2  ( 225 = 144 + 81 = 225).

So by the Inverse of Pythagoras Theorem  it is a right triangle.

The given values of side makes a proper right angle triangle.

To determine if the three given side lengths, 9, 12, and 15, form a right triangle, we can use the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's check if this holds true for the given side lengths:

[tex]9^2 + 12^2 = 81 + 144 = 225\\\\15^2 = 225[/tex]

The sum of the squares of the two shorter sides, 9 and 12, is equal to the square of the longest side, 15. This satisfies the Pythagorean theorem.

Therefore, the side lengths 9, 12, and 15 do form a right triangle.

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Answer:

7a

Step-by-step explanation:

Answer: 200

Step-by-step explanation:

First I would do it like this.

12.5

X. 16

—————-

6 times 5 is 0, carry the 3, 6 times 2 is 12 and add 3 from the other which is 15, put the 1 from the 15 to the one next to the 12. 6 times 1 is 6 plus 1 is 7 which now you have 750. 5 times 1 is 5, 2 times 1 is 2, 1 times 1 is 1. It should look like this now.

12.5

X 16

—————

750

+ 1250

——————-

Which is 8750 but wait. Where is the decimal? Well, there is only one number behind the decimal so it is 875.0 or 875.

Correct option B)[tex]63.4km^2[/tex] .

Step-by-step explanation:

We have the following figure attached as shown below.

Now, this triangular prism have 2 similar right angled surfaces and 3 rectangular surfaces , Let's calculate area for all of them:

2 similar right angled surfaces

We know that area of triangle = [tex]\frac{1}{2} b(h)[/tex]

⇒ [tex]area = \frac{1}{2} b(h)[/tex]

⇒ [tex]area = \frac{1}{2} (3.6)(7.7)[/tex]

⇒ [tex]area = 13.86km^{2}[/tex]

But there 2 such surfaces so , [tex]area = 2(13.86) = 27.72km^2[/tex]

3 rectangular surfaces

Area of rectangle = [tex]length(breadth)[/tex]

⇒ [tex]area_1 = 3.6(1.8)[/tex]

⇒ [tex]area_1 = 6.48km^2[/tex]

⇒ [tex]area_2= 7.7(1.8)[/tex]

⇒ [tex]area_2 = 13.86km^2[/tex]

⇒ [tex]area_3 = 8.5(1.8)[/tex]

⇒ [tex]area_2 = 15.3km^2[/tex]

Total area =[tex]6.48 + 13.86 + 15.3 = 35.64km^2[/tex]

Adding area of 2 similar right angled surfaces & 3 rectangular surfaces:

[tex]Area = 27.72+35.64 = 63.36km^2[/tex] = [tex]63.4km^2[/tex]

Correct option B)[tex]63.4km^2[/tex] .

Answer:

It is B.

Step-by-step explanation:

Trust me it's B

The Elijah have been on the soccer team for 8 years.

Step-by-step explanation:

Let,

Given that,

The boys have been on the soccer team for 10 years.

Number of years of Deaundre + Number of years of Eliijah = 10 years.

x + (5x-2) = 10

Keep x terms on one side and constants on another side to solve for x value :

6x = 10+2

6x = 12

x = 12/6

x = 2

The Deaundre have been on the soccer team for 2 years.

Substitute x=2 in (5x-2) to find the number of years of Elijah,

5(2)-2 = 8 years.

Therefore, the Elijah have been on the soccer team for 8 years.

Answer:

00.300

Step-by-step explanation:

What value does the 3 represent in the number 16.344

The 3 in the number 16.344 represents 0.003, since it's located on the third decimal place. It contributes three-thousandths to the total value. The position of the number changes the value it represents.

The value of 3 in the number 16.344 is represented as 0.003 in decimal place value. This is because it is situated in the third digit after the decimal point, signifying that it contributes the amount equal to three thousandths (0.003) to the total value of the number. For example, in using the concept of Six significant figures, we can say the number 16.344 has five significant figures, that is, the digits that give us precise information about the magnitude of the number - these digits being 1, 6, 3, 4 and 4.

It's also worthwhile to note that the placement of the digit 3 in the number 16.344 is different from a 3 that is located at other decimal places. For instance, if we look at the number 16.3443, the second 3 after the decimal point represents three ten-thousandths (0.0003) contribution to the total value of the number.

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The value of [tex](f+g)(18500)[/tex] is [tex]\Dollar 16675[/tex] dollars.

The interest he earns on x dollars invested in the first account is given by,

                     [tex]f(x)=0.05x[/tex]

The interest he earns from the second account,

                   [tex]g(x)=0.075(x+2500)[/tex]

[tex]f(x)+g(x)=0.05x+0.75(x+2500)\\\\f(x)+g(x)=0.05x+0.75x+1875\\\\f(x)+g(x)==0.8x+1875\\\\(f+g)(18500)=(0.8*18500)+1875\\\\f(x)+g(x)=14800+1875\\\\f(x)+g(x)=16675[/tex]

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Answer:

the answer was 24

Step-by-step explanation:

Final answer:

The product 1/2 x 1/3 equals 1/6, which can be visualized using a two-dimensional model where a rectangle is divided into halves and then thirds, resulting in 1/6 of the total area.

Explanation:

The product 1/2  times 1/3 can be understood through a two-dimensional model. If you take a rectangle and divide it into 2 equal parts, taking 1/2 of the whole, and then divide one of those halves into 3 equal parts, taking 1/3 of that half, you will have 1 out of the 6 equal parts of the original rectangle, which is 1/6, the product of 1/2 and 1/3.

To visualize this process, imagine a bar or a piece of chocolate that is first divided down the middle, and then one of those halves is divided into 3 equal pieces.

Taking one of these smaller pieces represents 1/6 of the original chocolate bar. In mathematical terms, when we multiply fractions, we multiply the numerators ( 1 times 1) to get the numerator of the product, and the denominators (2 times 3) to get the denominator of the product, yielding 1/6 as the answer. This demonstrates the first partial product principle, where in this case the third vector (1/3) is multiplied by the scalar product of 1/2.