Amadou built a toy box in the shape of a rectangular prism with an open top. The
diagram below shows the toy box and a net of the toy box.

According to the equation the given all necessary math work are:

\(A: (x -f)^2 +(y -g)^2 = h^2\)

B:  domain: [-5, 11]; range: [-9, 7]

C:  yes, inside

The hypοtenuse's square is equal tο the sum οf the squares οf the οther twο sides if a triangle has a straight angle (90 degrees), accοrding tο the Pythagοras theοrem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this. Base AB, height AC, and hypοtenuse BC are all used in this equatiοn. The lοngest side οf a right-angled triangle is its hypοtenuse, it shοuld be emphasized.

Part A:

Use οf the Pythagοrean theοrem gets yοu tο the equatiοn fοr a circle in essentially οne step:

sum οf squares οf sides = square οf hypοtenuse

\((x -f)^2 +(y -g)^2 = h^2\) . . . . . . circle cantered οn (f, g) with radius h

Part B:

The circle will be defined fοr values οf x in the dοmain f ± h, and fοr values οf y in the range g ± h.

dοmain: 3 ± 8 = [-5, 11]

range: -1 ±8 = [-9, 7]

Part C:

The distance frοm pοint (10, -4) tο (f, g) is ...

\(h^2 = (10 -3)^2 +(-4 -(-1))^2\)

\(h^2 = 7^2 +(-3)^2 = 49 +9 = 58\)

h = √58 < 8 . . . . the distance tο the pοint is less than h=8.

The pοint is inside the circle.

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The required rates are: Unit rate of graph K = 3, Unit rate of graph P = 0.5, and Unit rate of graph F = 1. The order from lower to greater is Graph P, graph F, graph K

Step 1: As we know that Unit Rate

Step 2: Notice that the in graph K line passes through the point (1,3)

Step 3: (1,3)

It means the value of function is 3 when x= 1

Step 4: So the unit rate of graph K is, 3/1

Step 5: Simplify the expression.

3/1 = 3

Step 6: Similarly we can see that the graph P have the point (2, 1)

Step 7: So the unit rate of graph P will be 1/2

Step 8: Simplify the expression.

1/2 = 0.5

Step 9: The graph F have point (1, 1) so it have unit rate of 1/1

Step 10: Simplify the expression.

1/1 = 1

Step 11: So we have unit rate of graph K = 3, F= 1 and graph P = 0.5

Step 12: Putting them in least to greater order as,

0.5, 1, 3

It follows that;

graph P, graph F, graph K

Therefore, the required answer is,

Unit rate of graph K = 3

Unit rate of graph P = 0.5

Unit rate of graph F = 1

And the order from lower to greater is, Graph P, graph F, graph K

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The number of nails in each box is: 1300, 1400, 600, 1200, and 500

Given 5000 nails in five boxes.

Let X denote the universal set.

Then n(X) = 5000.

Let A denote the first box,

B denote the second box,

C denote the third box,

D denote the fourth box, and

E denotes the fifth box.

The first and second boxes have 2700 nails altogether.

⇒n(A ∪ B) = 2700

The second and third boxes have 2000 nails altogether.

⇒n(B ∪ C) = 2000

The third and fourth boxes have 1800 nails altogether.

⇒n(C ∪ D) = 1800

The fourth and fifth boxes have 1700 nails altogether.

⇒n(D ∪ E) = 1700

We need to find out how many nails are there in each box.

That is to find out: n(A), n(B), n(C), n(D), and n(E).

Note that all these five sets are disjoint. This means that the intersection is empty.

n(A ∪ B ∪ C ∪ D) = n(A ∪ B) + n(C ∪ D) = 2700 + 1800 = 4500

n(E) = n(X) - n(A ∪ B ∪ C ∪ D) = 5000 - 4500 = 500

n(D) = n(D ∪ E) - n(E) = 1700 - 500 = 1200

n(C) = n(C ∪ D) - n(D) = 1800 - 1200 = 600

n(B) = n(B U C) - n(C) = 2000 - 600 = 1400

n(A) = n(A U B) - n(B) = 2700 - 1400 = 1300

Therefore, the number of nails in each box is 1300, 1400, 600, 1200, and 500.

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The expression that is equivalent to \(80^{(1/4}\) * x is \(80^{4/x}\)

To determine the equivalent expression to \(80^{1/4}\) * x, let's analyze each option:

\(80/4^{x}\)

This expression simplifies to \(20^{x}\), but it is not equivalent to the original expression.

Applying the power of a power rule, this expression simplifies to \(80^{x/4}\) , which is not equivalent to the original expression.

\(80/x^{4}\)

This expression can be simplified as \(80^{4 x^{4} }\) , which is not equivalent to the original expression.

Therefore, the expression that is option d.

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Answer:

Trapezoid

Step-by-step explanation:

It's a quadrilateral and it only has one pair of parallel sides.

Answer:

my guess would be the last one City to professional sports team but could be wrong

The missing statement is the quadratic formula and the correct option therefore is the third option;

The quadratic formula is used to find the solution of a quadratic equation. The quadratic formula is; \(x = \frac{-b\pm\sqrt{b^2-4\cdot a\cdot c} }{2\cdot a}\)

The statements and reasons can be presented algebraically as follows;

Statements \({}\)                                          Reasons

\(x^2+\frac{b}{a}\cdot x+(\frac{b}{2\cdot a} )^2 = -\frac{4\cdot a\cdot c}{4\cdot a^2}+ \frac{b^2}{4\cdot a^2}\)        Find a common denominator on the

                                                            right side of the equation

\(x^2 + \frac{b}{a} \cdot x+(\frac{b}{2\cdot a} )^2 = \frac{b^2-4\cdot a \cdot c}{4\cdot a^2}\)                 Add the fractions together on the

                                                     \({}\)        right side of the equation

\((x +\frac{b}{2\cdot a} )^2 = \frac{b^2 - 4\cdot a \cdot c}{4\cdot a^2}\)                             Rewrite the perfect squared equation

                                                      \({}\)      to the left side of the equation as a

                                                        \({}\)    binomial squared

\(x + \frac{b}{2\cdot a} = \pm\sqrt{\frac{b^2 - 4\cdot a \cdot c}{4\cdot a^2} }\)                   Take the square root of both sides of  the

                                                    \({}\) equation

\(\underline{x = \frac{-b\pm\sqrt{b^2 - 4\cdot a \cdot c} }{2\cdot a}}\)                                 Simplify the right side of the equation    

The correct option is therefore;

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Answer:

A

Step-by-step explanation:

i took the test

have a great day :) .!

Answer:

x = 7.69

Step-by-step explanation:

We need to solve the given problem. It is as follows :

175+14.25x=200+11x

Here, x is a variable. We can take on one side of an equation and constants to the other side such that,

14.25x-11x = 200-175

3.25x=25

x = 25/3.25

x = 7.69

Hence, the solution of the given equation is 7.69.

Answer:

-58

Step-by-step explanation:

20(-2) - 6 + 6(-2)

-40 - 6 - 12

-46 - 12

-58

The product of 5 × 5ab × 5, a, b is 125ab5 when written in its most Simple form

The expression 5 × 5ab × 5, a, b is equal to 125ab5. The reasoning is that when we multiply 5 by 5ab, we get 25ab, which we then multiply by 5 to get 125ab. Since a, b are variables, the product 125ab5 is the product of 5 × 5ab × 5, a, b, when written in its most simple form.

The expression 5 × 5ab × 5, a, b is an algebraic expression, which consists of numbers, variables, and operators. Variables are usually represented by letters or other symbols, while operators such as +, -, ×, ÷, ^ are used to indicate mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. In algebra, expressions can be simplified by combining like terms, expanding brackets, and applying other rules of arithmetic.

The most simple form of an expression is the one that cannot be further simplified.In the given expression, 5 × 5ab × 5, a, b, we can see that the number 5 appears three times, so we can simplify the expression by multiplying the numbers together.

Similarly, we can multiply the variables a and b together to get the term ab. Finally, we write the result as 125ab5, which is the product of 5 × 5ab × 5, a, b, in its most simple form.

Therefore, the product of 5 × 5ab × 5, a, b is 125ab5 when written in its most simple form.

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Selecting a fish special belongs to event F

3 is an odd number and it belongs to event O

Thus, for selecting a fish special number 3 is the outcome of events F and O

Answer: No

Step-by-step explanation:

to be proportional, both numbers have to increase by the same number

because if u multiply 6 by 2 you get 12, but when you multiply 10 by 2 you get 20, not 60 it would be proportional if you said 6 and 10 in to 12 and 20 in

Hello!

miles driven = x

the initial cost = 29

f(x) = 29 + 0.35x

Answer:

x ≥ -2

Step-by-step explanation:

my teacher went over this with us

The area of the square is given as 100 square unit

You should be aware that the square has all its sides equal

The perpendicular from opposite vertices represent distance

The given vertices are

(2,2) and (10,8)

Using the formula for distance between two points

d=√(10-2)²+(8-2)²

d=√8²+6²

d = √64+36

d=√100

This implies that d=10

The area of a square is given as s²

Area = 10²

Atrea = 100 square units

In conclusion, the area of the square is 100 square units

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Translated question:

The vertices of a square ABCD are A(2,2) and B(10,8), Find the area of the square

hope this answer helps you dear....it's a parallel!

Answer:

x is greater than 4

Step-by-step explanation:

4x + 5 is greater than 13

you want to find out what x is

4 - 4 x + 5 is greater than 13 - 4 ( whatever you do to one side you have to do to the other)

x + 5 is greater than 9

x + 5 - 5 is greater than 9 - 5

x is greater than 4

answer:

£11.25

explanation:

2.75+1=3.75 this was one third so you have to multiply 3.75 by 3 so you get 11.25.

Answer:

a

Step-by-step explanation:

solve for y in one equation

2x + y = -4

y = -4 - 2x

plug y into the other equation

5x + 3y = -6

5x + 3(-4 - 2x) = -6

5x -12 -6x = -6

-x - 12 = -6

-x = 6

x = -6

plug x into the equation to find y

y = -4 - 2x

y = -4 - 2(-6)

y = 8

ordered pair: (-6,8)

The equation of the line having slope 0 and passing through (-3,-2) is f(x) = -2.

Any horizontal line has the same y-value for every point on the line. We are given that the line passes through the point (-3,-2). This means that f(-3) = -2, since the y-value of the point (-3,-2) corresponds to the value of the function at x = -3.

This is because no matter what x-value we plug into the function, the output (y-value) will always be -2. Therefore, the equation of the line in function notation is f(x) = -2.

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Answer:

12.04

Step-by-step explanation:

Find the number in the hundredth place  4  and look one place to the right for the rounding digit  1 . Round up if this number is greater than or equal to  5  and round down if it is less than  5 .

Answer:

For perimiter just add up all the sides

10+8+6=24

Hope This Helps!!!

Answer:

Step-by-step explanation:

A coin of 25 grams contains 16 grams of copper.

Then a coin hundred grams contains (100×16)/25 = 64 grams of copper.

Hence the percentage of copper in the coin is 64%.

*I hope that this answer will help you.

Step-by-step explanation:

nickel is  9 grams out of (9 + 16) = 25 grams by weight

    9 is what percent of 25?

            9 / 25  * 100% =    36%

Answer:

30 > x

Step-by-step explanation:

-13 > x-43

Add 43 to each side

-13+43 > x-43+43

30 > x

The fraction 1¹/₂ + ⁵/₇ = 2³/₁₄

Fractions are numbers written in the form a/b where a and b are integers and b ≠ 0.

Since we have the fractions 1¹/₂ and  ⁵/₇ and we want to compute the sum

1¹/₂ + ⁵/₇, we re-write the first fraction as an improper fraction.

So, 1¹/₂ = ³/₂

Now, re-writting the equation, we have

³/₂ + ⁵/₇

To find the sum, wetake the L.C.M of both numbers which 2 × 7 = 14.

So, we make both denominators equal to the L.C.M.

So,  

³/₂ × ⁷/₇ + ⁵/₇ × ²/₂ = ²¹/₁₄ + ¹⁰/₁₄

= (21 + 10)/14

= 31/14

= (28 + 3)/14

= 28/14 + 3/14

= 2 + 3/14

= 2³/₁₄

So, 1¹/₂ + ⁵/₇ = 2³/₁₄

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Yes, always.

A sequence is a function that takens a positive integer and maps it some other number. For any integer you plug into the sequence, you only ever get one output.