3. The width and length of a rectangle are
consecutive integers. If the perimeter of
the rectangle is 142 inches, find the width
and length of the rectangle.​

Answer:

Dividing the number of balloon animal per the time he takes to make them you get an average of how many animals per minute Fred the clown can make.20/15=1,3 animals per minuteSince 0,3 is not a complete animal, the correct answer would be "Fred the clown can make 1 animal in 1 minute

Answer: 15 : 20

               6 : 8

               45 : 60

Step-by-step explanation:

First, you have to divide both numbers by 15:

15//15 = 1

20/15 = 4/3

Now you know that Fred can create 4/3 animal balloons in 1 minute.

If he spent 6 minutes creating animal balloons, then he can create 6 times as many animal balloons:

4/3 x 6 = 8

Now that we figured out the first part, we need to figure out how many he can make in 45 minutes.

We can do this by doing the same thing as we did for the first part, except we multiply 4/3 by 45 minutes:

4/3 x 45 = 60

Now that we figured out both parts, we know that our final answer should be:

15 : 20

6 : 8

45 : 60

Hope this helped! <3

Answer:

Positive real numbers

Step-by-step explanation:

The domain is all the possible values of x.  Here, x represents the time that the ball falls.

Natural numbers are integers greater than 0 (1, 2, 3, etc.).  However, the time doesn't have to be an integer (for example, x=1.5).

Positive integers are the same as natural numbers.

Positive rational numbers are numbers greater than 0 that can be written as a ratio of integers (1/1, 3/2, 2/1, etc.).  However, the time can also be irrational (for example, x=√2).

Positive real numbers are numbers greater than 0 and not imaginary (don't contain √-1).  This is the correct domain of the function.

The domain for the function ƒ(x) = 1,000 - 16x^2 is Positive Real Numbers.

The domain for the function ƒ(x) = 1,000 - 16x^2 is a set of Positive Real Numbers. This is because in real-world situations, such as the height of an object, negative time values do not make sense, and the function itself involves squaring x, which ensures that the result is positive. Therefore, the appropriate set of numbers as the domain for this function would be Positive Real Numbers.

Most likely infinite? Just a guess.

Answer:

Step-by-step explanation:

The question says nothing about repetition, so I'm assuming that 943449 is OK,

This can be solved this way

9 10 10 10 10 9

810,000

Answer:

(1,-1)

That is the ordered pair where they cross.

Step-by-step explanation:

The solution of the system is where the pair of lines there cross at.

The intersection is in the fourth quadrant there so your guess should definitely be of the form (positive, negative).

Only one choice is that and it is B.

It really does look like they cross at (1,-1).

To describe how to get from the origin to the intersection, I would say you would need to travel right 1 unit and down 1 unit.

We can even plug in our pair into both equations and see if it works.

y=x-2

y=4x-5

So if we plug in (1,-1) and assuming it is a solution, then both equations will give us the same thing on both sides. Let's try it:

y=x-2

-1=1-2

-1=-1

That's the same thing on both sides.

y=4x-5

-1=4(1)-5

-1=4-5

-1=-1

Again that is the same thing on both sides.

(1,-1) is indeed our solution.

Both the graph and the verification told us that.

Answer:

1, -1

Step-by-step explanation:

A.P.E.X 2021

Answer:

* The shorter side is 270 feet

* The longer side is 540 feet

* The greatest possible area is 145800 feet²

Step-by-step explanation:

* Lets explain how to solve the problem

- There are 1080 feet of fencing to fence a rectangular garden

- One side of the garden is bounded by a river so it doesn't need

 any fencing

- Consider that the width of the rectangular garden is x and its length

 is y and one of the two lengths is bounded by the river

- The length of the fence = 2 width + length

∵ The width = x and the length = y

∴ The length of the fence = 2x + y

- The length of the fence = 1080 feet

∴ 2x + y = 1080

- Lets find y in terms of x

∵ 2x + y = 1080 ⇒ subtract 2x from both sides

∴ y = 1080 - 2x ⇒ (1)

- The area of the garden = Length × width

∴ The area of the garden is A = xy

- To find the greatest area we will differentiate the area of the garden

  with respect to x and equate the differentiation by zero to find the

  value of x which makes the area greatest

∵ A = xy

- Use equation (1) to substitute y by x

∵ y = 1080 -2x

∴ A = x(1080 - 2x)

∴ A = 1080x - 2x²

# Remember

- If y = ax^n, then dy/dx = a(n) x^(n-1)

- If y = ax, then dy/dx = a (because x^0 = 1)

∵ A = 1080x - 2x²

∴ dA/dx = 1080 - 2(2)x

∴ dA/dx = 1080 - 4x

- To find x equate dA/dx by 0

∴ 1080 - 4x = 0 ⇒ add 4x to both sides

∴ 1080 = 4x ⇒ divide both sides by 4

∴ x = 270

- Substitute the value of x in equation (1) to find the value of y

∵ y = 1080 - 2x

∴ y = 1080 - 2(270) = 1080 - 540 = 540

∴ y = 540

* The shorter side is 270 feet

* The longer side is 540 feet

∵ The area of the garden is A = xy

∴ The greatest area is A = 270 × 540 = 145800 feet²

* The greatest possible area is 145800 feet²

Answer:

False because on the left side of the equation you are adding 18 and 35 first and on the right you are multiplying 35 and 4 first. This will give you an unequal equation when solved.

Let's solve each side

(18+35)*4=212

but 18+(35*4)=158

Answer:

the line will pass through yellow and red

Answer:

C) m∠5 + m∠6 =180°

D) m∠2 + m∠3 = m∠6

E) m∠2 + m∠3 + m∠5 = 180°

Step-by-step explanation:

TRUST ME! JUST TOOK MY QUIZ ON E2020

The correct equations are:

m∠2 + m∠3 + m∠5 = 180°

m∠2 + m∠5 =  m∠4

m∠5 + m∠6 = 180°

m∠2 + m∠3 =  m∠6

Equation is an expression used to show the relationship between two or more numbers and variables.

From the diagram:

m∠2 + m∠3 + m∠5 = 180° (sum of angles in a triangle)

But:

m∠3 + m∠4 = 180° (angle in a straight line)  

m∠2 + m∠3 + m∠5 = m∠3 + m∠4

m∠2 + m∠5 =  m∠4

Also:

m∠5 + m∠6 = 180° (angle in a straight line)

But:

m∠2 + m∠3 + m∠5 = 180

m∠2 + m∠3 + m∠5 = m∠5 + m∠6

m∠2 + m∠3 =  m∠6

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To expand and simplify the expression 4(2x+3)+4(3x+2), distribute the 4 to both sets of parentheses and combine like terms to get 20x + 20.

To expand and simplify the expression 4(2x+3)+4(3x+2), we can use the distributive property of multiplication over addition. The distributive property states that for any numbers a, b, and c, a(b+c) = ab+ac.

First, we distribute the 4 to both terms inside the first set of parentheses: 4 * 2x + 4 * 3. This simplifies to 8x + 12. Then, we distribute the 4 to both terms inside the second set of parentheses: 4 * 3x + 4 * 2. This simplifies to 12x + 8.

Combining the like terms, the final simplified expression is: 8x + 12 + 12x + 8 = 20x + 20.

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Answer:

[tex]\large\boxed{f^{-1}(x)=9x-18}[/tex]

Step-by-step explanation:

[tex]f(x)=\dfrac{1}{9}x+2\to y=\dfrac{1}{9}x+2\\\\\text{exchange x to y and vice versa}\\\\x=\dfrac{1}{9}y+2\\\\\text{solve for y}\\\\\dfrac{1}{9}y+2=x\qquad\text{subtract 2 from both sides}\\\\\dfrac{1}{9}y=x-2\qquad\text{multiply both sides by 9}\\\\9\!\!\!\!\diagup^1\cdot\dfrac{1}{9\!\!\!\!\diagup_1}y=9x-(9)(2)\\\\y=9x-18[/tex]

Answer:

30 times

Step-by-step explanation:

Weight of adult blue whale = [tex]9 \times 10^{4}[/tex] kilogram

Weight of an elephant = [tex]3 \times 10^{3}[/tex] kilogram

In order to find how many times a quantity is as compared to the other quantity, we divide the two. So here we have to divide the weight of adult blue whale by the wight of elephant.

[tex]\frac{9 \times 10^{4}}{3 \times 10^{3}}\\= 30[/tex]

This means, adult blue whale is 30 times heavier than the elephant.

[tex](9x-4)-(3x+2)=9x-4-3x-2=6x-6[/tex]

Answer:

4  3/8

Step-by-step explanation:

1 7/8 × 2 1/3

Change the numbers to improper fractions

1 7/8 = (8*1 +7) /8 = 15/8

2 1/3 = (3*2 +1)/3 = 7/3

15/8 * 7/3

Rearranging

15/3 * 7/8

5/1 * 7/8

35/8

Now we need to change this back to a mixed number

8 goes into 35   4 times with 3 left over

4 3/8

Answer:

35/8 or 4 3/8

Step-by-step explanation:

Change each fraction to improper

15/8 * 7/3

multiply

105/24

reduce

35/8

make it mixed if the answer wants it to be

4 3/8

[tex]\bf \textit{height or altitude of an equilateral triangle}\\\\ h=\cfrac{s\sqrt{3}}{2}~~ \begin{cases} s=\stackrel{length~of}{a~side}\\ \cline{1-1} s=8\sqrt{3} \end{cases}\implies h=\cfrac{8\sqrt{3}\cdot \sqrt{3}}{2}\implies h=\cfrac{8\sqrt{3^2}}{2} \\\\\\ h=4\cdot 3\implies h=12[/tex]

Answer:

[tex]\large\boxed{a_n=2(-4)^{n-1}=\dfrac{(-4)^n}{2}}[/tex]

Step-by-step explanation:

The explicit equation of a geometric sequence:

[tex]a_n=a_1r^{n-1}[/tex]

The domain is the set of all Counting Numbers.

We have the first term of [tex]a_1=2[/tex] and the second term of [tex]a_2=-8[/tex].

Calculate the common ratio r:

[tex]r=\dfrac{a_{n-1}}{a_2}\to r=\dfrac{a_2}{a_1}[/tex]

Substitute:

[tex]r=\dfrac{-8}{2}=-4[/tex]

[tex]a_n=(2)(-4)^{n-1}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\a_n=(2\!\!\!\!\diagup^1)\left(\dfrac{(-4)^n}{4\!\!\!\!\diagup_2}\right)\\\\a_n=\dfrac{(-4)^n}{2}[/tex]

Answer:

Step-by-step explanation:

A geometric sequence has a common ratio. in this case the common ratio

r = -8/2 = -4.

The explicit formula is an = 2(-4)^(n-1).

Answer:

4(x - 5)(x + 3)

Step-by-step explanation:

Given

4x² - 8x - 60 ← factor out 4 from each term

= 4(x² - 2x - 15)

To factor the quadratic

Consider the factors of the constant term ( - 15) which sum to give the coefficient of the x- term ( - 2)

The factors are - 5 and + 3, since

- 5 × 3 = - 15 and - 5 + 3 = - 2, hence

x² - 2x - 15 = (x - 5)(x + 3) and

4x² - 8x - 60 = 4(x - 5)(x + 3)

Answer:

I don't know what the following sentence is:

But D is the equation to represent the situation

and A is what turns out to be his current age.

(If you want more help, on this question please post the following sentence).

Step-by-step explanation:

Let x represent the current age.

15 years from now his age is 3 times his age 5 years ago means we have the equation:

x+15=3(x-5)

(I added x to 15 because we said 15 years in the future)

Let's solve this to see if makes any sense just for fun:

Distribute:

x+15=3x-15

Add 15 on both sides:

x+30=3x

Subtract x on both sides:

   30=2x

Divide both sides by 2:

   15=x

So this means his current age is 15.

5 years ago his age would have been 10.

15 years in the future his age will be 30.

Is 30 equal to 3 times 10? Yes, it is! The equation does make sense.

Answer:

D,

Step-by-step explanation:

x is the present age of William, 15 years from now is x+15, and that is equal to  3 times 3() the age he had 5 years ago (x-5)., the equation is  x+15=3(x-5)

Answer:

2^ (-1)

1/2

Step-by-step explanation:

Add the exponents which have common bases.

3 + (-4) = -1

2^ (-1)

1 / 2

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Answer:

The simplified form of the provided expression is [tex]2^{-1}\ or\ \frac{1}{2}[/tex]

Step-by-step explanation:

Consider the provided expression:

[tex](2^3)(2^{-4})[/tex]

Use the product rule of exponent:

[tex]a^m \cdot a^n=a^{m+n}[/tex]

Now use the above formula to simplify the provided expression.

[tex](2^3)(2^{-4})=2^{3+(-4)}[/tex]

[tex](2^3)(2^{-4})=2^{3-4}[/tex]

[tex](2^3)(2^{-4})=2^{-1}[/tex]

Hence, the simplified form of the provided expression is [tex]2^{-1}\ or\ \frac{1}{2}[/tex]

The probability that a player wins the game by adding the numbers from the slips drawn from the box is 40%. If the rule changes and the player multiplies the numbers instead of adding them, the winning probability increases to 70%.

The game consists of drawing two numbers from the box and verifying whether their sum or product is even or odd. In Mathematics, for the sum to be even, both numbers must be odd or both must be even. If we check, we have 2 odd numbers (7, 9) and 3 even numbers (4, 6, 8). The combinations for even sum could be odd-odd or even-even. The total successful events would be 1 (odd-odd) + 3 (even-even) = 4 out of total 10 possible events (5C2), which gives us the probability of the player winning the game as 4/10 or 40%

Now, whether the probability changes when we multiply instead of adding: Yes, it does! In Mathematics, an even number results when multiplying any number by an even number, regardless of whether the other number is odd or even. Therefore, since 3 out of 5 numbers are even, the probability that the player wins if they multiply the two numbers they select instead of adding them is greater, confirmed by calculating combinations again and we find 7 out of 10 possible events yield an even product, therefore probability is 70%, which is greater than that of adding them.

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Answer:

A.) $56

Step-by-step explanation:

1.  Convert 7% into the numerical version by either

    A. Moving the decimal two spaces to the right, giving us .07

                                               or

    B. Making 7% into a fraction, 7/100

2. Now make an equation with the total amount of money (M) multiplied by the interest (P) inside of parenthesis. This will give us 7% of $800 in your case.

                                        (800 × .07) → 56

3.  Then, multiply by the number of years the interest has been accumulated.

                                              56 × 1

The official equation for this is: a = p(1 + r)^t

a = amount at end (initial amount + interest gained)

p = initial amount

r = rate (percent interest)

t = time in years

The correct option will be option A: Man will receive $56 interest in a year.

Simple Interest amount can be calculated by the product of principal amount, rate of interest, and time.

Simple Interest= S.I. =p*t*r/100

where p is the principal amount,

r is interest rate (in %)

t is the time (in year).

Here, given,

principal amount P = $800

rate of interest= r=7%

time=t=1 year

using the above formula,

Simple Interest S.I.= p*t*r/100= (800*1*7)/100= $56

Therefore man will receive $56 interest in a year.

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Answer:

Part A)

This quadratic expression can be factored by using the difference of squares pattern.

Part B) (5x+y) and (5x-y)

Step-by-step explanation:

Given:

25x^2-y^2

above polynomial can be factorize by using difference of squares formula

a2-b2=(a+b)(a-b)

25x^2-y^2= (5x-y)(5x+y)

so for part A)

correct option is  This quadratic expression can be factored by using the difference of squares pattern.

Part B)

As factored above in part A,

the factors of given polynomial 25x^2-y^2 are (5x+y)(5x-y)

so for part B) correct options are (5x+y) and (5x-y) !

Answer:

-6 - (-8) = 2.

Your number line might have a bubble at 2. Or it may show movement 8 units to the right of -6. Whatever it is, you should end up at the value of 2.

Step-by-step explanation:

We don't see a number line, but I can still show how to solve.

-6 - (-8) is the same as doing negative six plus negative one times negative 8. Or in number terms it would look like:

-6 + (- 1(- 8))

In the order of operations -- PEMDAS -- we do parenthesis first.

- 1( - 8) = 8, so we simplify by plugging this value back into the equation:

-6 + 8

-6 + 8 is the same as 8 - 6.

8 - 6 = 2

Your answer is 2.

Since the example circle is not shown, I can not answer thoroughly, but I will try my best.

The equation of a circle: (x - h)² + (y - k)² = r², where (h,k) is the center and r is the radius of the circle.

This means that for the radius to be two units, the right side of the equation is 2² = 4. So either B or d can be right.

Depending on the center of the given circle, we could narrow down to our final answer. If the center is (4,5), B is right, and if (5,4) is the center, D is right.

Due to the fact the example circle isn't proven, I can't solution thoroughly, but I will attempt my exceptional.

The equation of a circle: (x - h)² + (y - okay)² = r²,

in which (h, ok) is in the middle and r is the radius of the circle.

this means that for the radius to be two devices, the proper facet of the equation is two² = four. So either B or d can be right.

depending on the centre of the given circle, we ought to narrow right down to our very last answer. If the centre is (4, five), B is right, and if (five, four) is in the middle, D is proper.

The equation for a circle is given by:

(x-h)2+(y-k)2 = a2

Where (h,k) is the centre and a is the radius of the circle.

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Answer:

8100

Step-by-step explanation:

Step-by-step explanation:

We want to find the length of the square's diagonal.  Since the square has right angles, we can use Pythagorean theorem.

c² = a² + b²

x² = 90² + 90²

x = 90√2

x ≈ 127.3 feet

The vertices of the triangle are the points where any pair of lines intersect.

We start by setting up the system

[tex]\begin{cases}y=-x+2\\y=2x-1 \end{cases} \iff -x+2=2x-1 \iff 3x=3 \iff x=1[/tex]

Using one of the two equations we can derive the correspondent y value:

[tex]f(x)=-x+2 \implies f(1)=-1+2 = 1[/tex]

So, one vertex is (1, 1)

We choose the other two pairs of lines to find the other vertices:

[tex]\begin{cases}y=-x+2\\y=x-2 \end{cases} \iff -x+2=x-2 \iff x=2 \implies y = 0[/tex]

[tex]\begin{cases}y=x-2\\y=2x-1 \end{cases} \iff x-2=2x-1 \iff x=-1 \implies y=-3[/tex]

So, the three vertices are (1, 1), (2, 0), (-1, -3).

Answer:

(1, 1), (2, 0), and (-1, -3)

Step-by-step explanation:

I got right on the test.

Answer:

First exercise: [tex]x=7[/tex]

Second exercise: [tex]x=2[/tex]

Step-by-step explanation:

Acording to the Intersecting Secants Theorem the products of the segments of two secants that intersect each other outside a circle, are equal.

Based on this, in order to solve the first exercise and the second exercise, we can write  the following expressions and solve for "x":

First exercise:

[tex](5)(5+x)=6(6+4)\\\\25+5x=60\\\\5x=60-25\\\\x=\frac{35}{5}\\\\x=7[/tex]

Second exercise:

[tex](4)(4+x)=3(3+5)\\\\16+4x=24\\\\4x=24-16\\\\x=\frac{8}{4}\\\\x=2[/tex]

Answer:

its simplest form is 4/5