Question 12
4
Which of the following numbers is irrational?
-9
5
7
√√5. √9
3

One of the boards is 30 inches long and the other board is 12 inches longer so it has to be 42 inches long. The sum of the lengths of the two boards is 72 cm and one of the boards is 12 inches longer than the other.

Here,

A board is 72 cm in length and must be cut so that one piece is 12 cm longer than the other piece .

We have to find the leg of each piece.

What is Length, Width and height?

The length, width and  height of an object are the different dimensions in linear units. length is the longest side of a shape, width is the shorter side, and height is the vertical dimension of the shape.

Now,

If you're going to cut the 72 inch board into two pieces, you can call one of the pieces x units long.

And, since the other piece is 12 inches longer than your first piece, its length is x + 12.

And, when you place these two pieces back together, their lengths should add up to be 72 inches.

You can write this last statement about adding the two pieces together to get a 72 inch piece

In equation form as:

x + (x+12) = 72

2x + 12 = 72

To solve this begin by subtracting 12 from both sides;

2x = 60

Now just divide both sides by 2 to find that:

x = 30

So, one of the boards is 30 inches long and the other board is 12 inches longer so it has to be 42 inches long. The sum of the lengths of the two boards is 72 cm and one of the boards is 12 inches longer than the other.

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Answer:

A)  |x - 1200| = 22

B)  x = 1222,  x = 1178

C)  Minimum = $1,178

    Maximum = $1,222

Step-by-step explanation:

Define the variable:

Given information:

If the artist plans to sell $300 of prints each week, then she plans to sell approx $1200 of prints each month, since there are approximately 4 weeks in each month.

If she is within $22 of her goal, this month then:

⇒ |x - 1200| = 22

To solve an equation containing an absolute value, set the contents of the absolute value equal to both the positive and negative value of the number on the other side of the equation, then solve both equations:

Equation 1

⇒ x - 1200 = 22

⇒ x - 1200 + 1200 = 22 + 1200

⇒ x = 1222

Equation 2

⇒ x - 1200 = -22

⇒ x - 1200 + 1200 = -22 + 1200

⇒ x = 1178

Therefore:

Answer:

look for patterns also, Ann purchased 12 apples

Step-by-step explanation:

x apples

1/3 of x, (x - x/3) = (3x - x) /3 = 2x/3

Number of people who shared (2x/3) = 4 with each getting 2Total number shared = 4 * 2 = 8Fraction shared = total shared2x/3 = 8Multiply both sides by 3(2x/3) * 3 = 8 * 32x = 24x = 12

The monthly installments need to be paid is $10995.

To determine the number of months needed to pay off the remaining balance. We need to know the monthly installment.

When you get an installment loan, you get the money you borrowed or the item you bought right away.

Now, as per the question;

Amount paid in cash = $1500

Remaining balance which is to be paid as monthly installments

= $12495 - $1500

=$12495 − $1500

=$10995

Thus, the monthly installments are $10995.

Now, to determine the number of months needed to pay off the remaining balance. The monthly installment is need to be known.

As a result, information on monthly installments is lacking.

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The complete question is-

What necessary piece of information is missing that prevents solving the problem? By paying $1500 cash and the balance in equal monthly payments, how many months would it take to pay for a car costing$12,495?

Answer:no

Step-by-step explanation:

sides ab and de are equivalent and sides fd and ca are equivalent but when it comes to sides bc and ef they are not with the scale factor as 2

Answer:

xxx 20

Step-by-step explanation:

Answer:

thyjdbbdhehwjwnwjehe

Answer:

y=(3/4)x - (3/2)

Step-by-step explanation:

3x−4y=6

isolate the y variable

-4y=-3x+6

divide by -4

y=(3/4)x - (3/2)

it is equivalent because it is the same equation just in a different form

Answer: No.

Step-by-step explanation: The sides are all different. Therefore, it cannot be a right angle.

(i think)

Answer:

Yes.

Step-by-step explanation:

By converse of Pythagoras' Theorem,

[tex]5 {}^{2} = 4 {}^{2} + 3 {}^{2} [/tex]

25 = 16 + 9

Therefore, the triangle is a right-angled triangle.

Hope this helped! ^^

Answer:

102

Step-by-step explanation:

x = 5th test

(82 + 76 + 90 + 0 + x) /5 = 70

248 + x = 70*5

x = 350 - 248

x = 102

Three principles of experimental design: Control, Random, Enough.

What is the principle of an experiment?

The guiding principles of experimental designs are randomization, replication, and local control. These recommendations offer a valid test of significance.

What are the three experimental design principles, and can you briefly describe how each one reduces experimental error?

How many experimental design principles are there?

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All values of y in the simplest form are 3 and -3

The equation is given as

21 = |7y|

The above equation is an absolute value equation

When the above equation is expanded, we have the following equations

So, we have

-21 = 7y and 21 = 7y

Divide both sides of the equations by 7

So, we have

-3 = y and 3 = y

Rewrite as

So, we have

y = -3 and y = 3

Hence, all values of y in the simplest form are 3 and -3

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Answer:

Step-by-step explanation:

2/5 or 4/10 or 8/20 or 16/40  

The expression of 15km as a percentage of 120km as required in the task content is; 12.5%

Since it follows from convention that a percentage is a representation of an entity as a fraction of a hundred partitions.

On this note, the percentage representation is such that;

15km of 120km is;

(15/120) × 100%

0.125 × 100%

= 12.5%.

Ultimately, 15km is 12.5% of 120km.

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The minimum and maximum allowed baseball masses are 143 grams and 147 grams

The given parameters are

Mass = 145 grams

Vary = 2 grams

This means that the allowed baseball masses are

Allowed baseball masses = Mass  ± Vary

This gives

Allowed baseball masses = (145 - 2, 145 + 2) grams

Evaluate

Allowed baseball masses = 143 grams, 147 grams

Hence, the minimum and maximum allowed baseball masses are 143 grams and 147 grams

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The simple interest was $10.5 and the amount after 1 year would be $360.5 in her account.

Simple interest is defined as interest paid on the original principal and calculated with the following formula:

S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100

We have been given data as

Principal amount (P) = $350

Time (T) = 1 year

The rate of interest (R) = 3%

Simple interest= P × R × T

Simple interest = 350 × 3/100 × 1

Simple interest = $10.5

So the amount after 1 year would be P + S.I. = 350 + 10.5 = $360.5

Therefore, the simple interest would be $10.5 and the amount after 1 year would be $360.5.

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4.05 with (05) repeating if converted to a fraction or mixed number will be

[tex]4\frac{5}{99}[/tex].

As per the question statement, we are provided with a repeating decimal, 4.05 with (05) repeating.

We are required to convert the repeating decimal into a mixed number.

To solve this question, we need to know the formula to convert any repeating decimal number to a fraction which goes as:

[tex]\frac{[(DN*F)-NRF]}{D}[/tex]

Where, DN denoted the concerned Decimal Number,

(F = 10) if one repeating is number, 100 if two repeating numbers, 1000 if three repeating numbers and so on.

NRP denotes the Non-repeating part of decimal number.

And, D = 9 if one repeating number, 99 if two repeating numbers, 999 if three repeating numbers, and so on, similar to F.

Then, using our given data in the above formula, we get

4.05 with (05) repeating = [tex]\frac{(4.05*100)-4}{99}=\frac{(405-4)}{99}=\frac{401}{99}=4\frac{5}{99}[/tex].

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Answer:

Step-by-step explanation:

The wavelength of the n = 4 standing wave is 3.5cm.

Standing Waves:

A standing wave is a stationary wave, which means that the wave oscillates in time but the peak amplitude does not move in space. This can happen in a stationary medium from an interference due to two waves traveling in opposite directions. For a harmonic wave, the string's displacement in the y-direction from the x-position and time t can be calculated by using the expression

y(x ,t)=2Asin(2πxλ)cos(ωt)

where A is the maximum displacement in the y-direction, λ

is the wavelength, and ω is the angular frequency. Given a taut string of length L, and assuming the the driving force is at x=0, the boundary conditions are

y(0,t)=0y(L, t)=2Asin(2πLλ)cos(ωt)=0

Given the latter boundary condition, a standing wave occurs when sin(2πLλ)=0=sin(nπ). The condition for the standing wave is then of the form n=2Lλ.

The condition where the standing wave occurs is given by the expression n=4Lλ, where n is a positive integer value, L is the string length, and λ is the wavelength. We calculate the wavelength of an n=4 standing wave as follows:

λ=4Ln=4(7 cm) / 2

= 14 /2

= 3.5cm.

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The vertex of the equation g(x) = I x ₊ 6 I is (₋6 , 0).

Given the equation is g(x) =  I x ₊ 6 I

The equation of the absolute value function  is:

y = I x ₋ h I ₊ k where (h , k) is the vertex.

When the input is 0, the vertical axis will be intersected by the graph of an absolute value function. The horizontal axis is not usually where they cross. Depending on how the graph has been moved and reflected, it may or may not cross the horizontal axis.

compare the given equation to the above form.

y = I x ₊ 6 I ₊ 0

y = I x ₋ (₋6) I ₊ 0

hence we (h,k) as (₋6 , 0)

Therefore the coordinates of the vertex are (₋6 , 0)

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Answer:

20%

Step-by-step explanation:

Every fifth car would be 1/5 or 20%

Answer: 7.247 x 10^6

Step-by-step explanation:

(7.26x10^6)-(1.3x10^4)

⇒ 7.247 x 10^6

Scientific notation of given expression = 7.247× 10⁶

Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.

For example,

650,000,000 can be written in scientific notation as 6.5 ✕ 10⁸.

Given expression

(7.26x10⁶)-(1.3x10⁴)

It can be written as

= (7.26×1000000) - (1.3 × 10000)

= 7260000 - 13000
= 7247000

= 7.247× 10⁶

Hence,  7.247× 10⁶ is the scientific notation of given expression.

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Answer:

Oh! WoW

Very nice questions .

Step-by-step explanation:

Please provide full question

When a washer and a dryer cost $995 combined. If  the washer cost $45 more than the dryer, then the cost of the dryer is $475

The combined cost of a washer and a dryer = $995

Consider the cost of a dryer as x

The washer cost $45 more than the dryer.

The cost of the washer = x+45

Then the equation will be

x+x+45 = 995

2x+45 = 995

2x = 950

x = 950/2

x = 475

The cost of the dryer is $475

Hence, when a washer and a dryer cost $995 combined. If  the washer cost $45 more than the dryer, then the cost of the dryer is $475

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Answer:

{y | 0 ≤ y < 9}

Step-by-step explanation:

The range is all the y-values; all the y's on the graph, or if you had an equation, all the y's that could be produced by that equation.

Right away, you know if the question is RANGE, the sets showing x are NOT the answer.

On the graph shown the lowest point is at (0,0) and it IS actually on the graph, so we use a >= symbol that has the "or equal to" bar under the > symbol.

The biggest y-value on the graph is the 9, but it's an open point, so exactly9 is technically NOT on the graph. So we use a < symbol without the bar underneath.

Answer:

x = 27

Step-by-step explanation:

(5x - 32) + (3x - 4) = 180

8x - 36 = 180

x = 216

x = 27

m<NQR = 5x - 32 = 5*27 - 32 = 103

m<QRP = 3x - 4 = 3*27 - 4 = 77

Answer:

29. 7r^2-5r-2

31. 15x^4-7x^3-2x^2

37. -3k^2-2km+5kn+m^2+mn-2n^2

43. 4m^2-9

5. 16x^4 - 25y^2

Step-by-step explanation:

To solve these you expand the polynomial and use the FOIL method.