A square floor has a side length of (9/2) units. A square tile has a side length of (3/2)² units. The square tiles will be placed ro tile the square floor. How many full tiles will it take to cover the floor?

Answer:

x = [tex]\frac{15-3y}{5}[/tex]

Step-by-step explanation:

5x + 3y = 15 ( isolate the term in x by subtracting 3y from both sides )

5x = 15 - 3y ( isolate x by dividing both sides by 5 )

x = [tex]\frac{15-3y}{5}[/tex]

The values of x and measures of angles are:

1. x = 12; m<PQS = 71°; m<PQT = 142°; m<TQR = 41°

2. x = 8; m<GDH = 126°; m<FDH = 200°; m<FDE = 137°

1. Since QS bisects angle PQT, therefore:

measure of angle PQS = measure of angle SQT

Given:

m<SQT = 8x - 25

m<PQT = 9x + 34

m<SQR = 112°

Thus:

m<PQT = 2(m<SQT)

Substitute

9x + 34 = 2(8x - 25)

9x + 34 = 16x - 50

9x - 16x = -34 - 50

-7x = -84

x = 12

m<PQS = m<SQT = 8x - 25

Plug in the value of x

m<PQS = 8x - 25 = 8(12) - 25

m<PQS = 71°

m<PQT = 9x + 34 = 9(12) + 34

m<PQT = 142°

m<TQR = m<SQR - m<SQT [angle addition theorem]

m<TQR = 112 - 71

m<TQR = 41°

2. Given:

m<GDE = 8x - 1

m<EDH = 6x + 15

m<CDF = 43

m<GDE = m<EDH [reason: DE bisects GDH]

Substitute

8x - 1 = 6x + 15

8x - 6x = 1 + 15

2x = 16

2x/2 = 16/2

x = 8

m<GDH = 2(m<GDE)

m<GDH = 2(8x - 1)

m<GDH = 16x - 2 = 16(8) - 2

m<GDH = 126°

m<FDG = 180 - m<CDF - m<GDE

m<FDG = 180 - 43 - (8x - 1)

m<FDG = 180 - 43 - (8(8) - 1)

m<FDG = 180 - 43 - 63

m<FDG = 74°

m<FDH = m<FDG + m<GDH

m<FDH = 74 + 126

m<FDH = 200°

m<FDE = m<FDG + m<GDE

m<FDE = 74 + 63

m<FDE = 137°

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Answer:

x=m/2+k , k≠-2

Step-by-step explanation:

2x+kx=m

Factor out x from the expression:

(2+k)x=m

Assume 2+k≠0 and divide both sides of the equation by 2+k:

x=m/2k , 2+k≠0

Rewrite the restriction:

x=m/2+k≠-2

Solution:

x=m/2+k , k≠-2

The value of x in the given expression is x = m / (k+2)

An expression is a mathematical statement containing variables, numerical, and they are related by at least one mathematical operation.

Given an expression, 2x + kx = m

We are asked to rearrange the values and find the value of x.

Therefore,

2x + kx = m

Since, two terms have same variable, therefore, taking x common from both,

x(2+k) = m

x(k+2) = m

Now, transpose (k+2) to right side, we get,

x = m / (k+2)

Hence, we get the value of x as, x = m / (k+2)

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The answer to this question is (gof)(x)=2x+7

According to question:

Given: f(x)=4 x, g(x)=1/2 x+7,h(x)=-2 x+4

We always simplify everything in brackets first using BODMAS. Therefore, in order to compute f(g(x)), g(x) must first be calculated and then substituted within f(x). Similar to this, in order to determine g(f(x)), f(x) must first be computed and then substituted in g(x). In other words, the sequence is important when locating the composite functions. It implies that g(f(x)) and f(g(x)) may not be equal. The following procedures are used to obtain the composite function f(g(a)) for any two functions f(x) and g(x).

By changing x = a in g, find g(a) (x).

Put x = g(a) into f to find f(g(a)) (x)

∴(gof)(x)=2x+7

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Answer:

A

Step-by-step explanation:

70-271=20

Answer: it's 7/10

Step-by-step explanation:

the 49 simplifies to 7, and the 100 simplifies to 10

Answer:

can you add a photo of the questions? So it's easier to see

The sum of its integer and fractional parts is 5 + (-7) + 1/3 + 2/3. Option D

Fractions are defined as part of a whole.

The types of fractions include:

Given the expression;

5 1/3 + -7 2/3

The integers are:

5 and -7

The fractions are;

1/3 and 2/3

The sum of the integers and fractional parts are;

5 + (-7) + 1/3 + 2/3

Thus, the sum of its integer and fractional parts is 5 + (-7) + 1/3 + 2/3. Option D

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Answer:

9x³y²

Step-by-step explanation:

To simplify, factorize 81 in powers of 2 ;  x⁶ in powers of 2 and y² in powers of 2.

[tex]\sf \sqrt{81x^6y^2}=\sqrt{9^2 * x^{3*2}*y^2}[/tex]

             [tex]\sf = \sqrt{9^2* (x^3)^2)* y^2}\\\\ = 9 * x^3*y^2\\\\=9x^3y^2[/tex]

A composite function exists as a function that depends on another function. The value of f(g(x)) = x-8 and g(f(x)) = x-2.

In mathematics, function composition exists as an operation ∘ that takes two functions f and g, and has a function h = g ∘ f such that h(x) = g. In this operation, the function g exists used to the result of applying the function f to x.

Function composition is a mathematical procedure where two functions, f, and g, are taken and a function, h = g ∘ f, is produced such that h(x) = g(f(x)). The function g exists used in this operation on the outcome of applying the function f to x.

Let the two functions be f(x) = x+3  and g(x) = x-5

f(g(x)) = f(x-5)

simplifying the above equation, we get

f(x-5) = x-5+3

f(g(x)) = x-8

g(f(x))  = g(x+3)

simplifying th above equation, we get

g(x+3) = x+3-5

g(x+3) = x-2

Therefore, the value of f(g(x)) = x-8 and g(f(x)) = x-2.

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According to the empirical​ rule,  95% will be within two standard deviations of the mean.

The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, almost all observed data will fall within three standard deviations (denoted by σ) of the mean or average (denoted by µ).

Under this rule, 68% of the data falls within one standard deviation, 95% percent within two standard deviations, and 99.7% within three standard deviations from the mean. Three-sigma limits that follow the empirical rule are used to set the upper and lower control limits in statistical quality control charts and in risk analysis such as VaR.

The empirical rule is used often in statistics for forecasting final outcomes. After calculating the standard deviation and before collecting exact data, this rule can be used as a rough estimate of the outcome of the impending data to be collected and analyzed.

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Answer:

x≥2

Step-by-step explanation:

-16≥ -8x

x≥2

a) The approximate sum of the numbers by first rounding each number is 74,600

b) The exact sum of the numbers rounded to the nearest hundred is 74,500

From the question, we are determine the approximate sum of the given numbers

The given numbers are

34,856 and 39,670

a) Round 34,856 to the nearest hundred

34,856 to the nearest hundred is 34,900

Also,

Round 39,670 to the nearest hundred

39,670 to the nearest hundred is 39,700

Now,

Add the rounded numbers

34,900 + 39,700 = 74,600

b) The exact sum of the numbers is

34,856 + 39,670 = 74,526

Rounding the result to the nearest hundred

74,526 rounded to the nearest hundred is 74,500

Hence, the exact sum of the numbers rounded to the nearest hundred is 74,500

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After solving the equation the value of r in 4 r²=3 is [tex]\sqrt{3/4}[/tex].

We have to find r in  4 r²=3

⇒ 4 r² = 3

⇒ r² = 3/4

⇒ r = [tex]\sqrt{3/4}[/tex]

So, r is equal to  [tex]\sqrt{3/4}[/tex]

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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Answer:

Step-by-step explanation:

Volume of the cube = 2*4*6 = 48 cm^3.

Its density is 24 g / cm^3

The density of water is 1g /cm^3 so it will sink in water.

A) The percentage represented in each picture is as follows:

A-1) 80%

A-2) 12.5%

A-3) 10%

B) The portion represented in each picture is written as a fraction as follows:

B-1) 80% = 8/10 or 4/5

B-2) 12.5% = 1.25/10 or 1/8

B-3) 10 = 1/10 or 2/20

A percentage is a fraction of 100.

A percentage is also a ratio, showing how much of the whole is contained by the portion.

Percentages are written with the percentage sign (%).

A-1) 80% for A 10 by 10 block of 100 where 8 columns of 10 are shaded.

A-2) 12.5% for A 10 by 10 block of 100 where the first row, and 2 and a half squares of the second row are shaded.

A-3) 10% for A 10 by 10 block of 100 where 1 row of 10 is shaded.

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The trinomial form of the given expression (2x-2)(2x+8) is 4x² + 12x - 16.

Given the expression in the question;

(2x-2)(2x+8)

Expand using FOIL Method.

Apply distributive property

(2x-2)(2x+8)

2x( 2x + 8 ) -2( 2x + 8 )

Apply distributive property

2x(2x) + 8(2x) -2(2x) + 8(-2)

Perform the operation

2x(2x) + 8(2x) -2(2x) + 8(-2)

4x² + 16x - 4x - 16

Combine like terms

4x² + 16x - 4x - 16

4x² + 12x - 16

Therefore, the trinomial form of the given expression (2x-2)(2x+8) is 4x² + 12x - 16.

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The composition of f and g, as (fog)(x) = f(g(x)) for functions f and g. g should be applied to x. If fog(x) = x and gof (x) = x for all x values in the domain of f and g, then they are inverse functions.

In mathematics, function composition is an operation in which two functions, f and g, generate a new function, h, in such a way that h(x) = g(f(x)). This means that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.

Define fog, the composition of f and g, as (fog)(x) = f(g(x)) for functions f and g. g should be applied to x. If fog(x) = x and gof (x) = x for all x values in the domain of f and g, then they are inverse functions.

In math, the domain (the x-values) of one function becomes the range (the y-value answers) of the next function. Composition notation is as follows: (f o g)(x) = f(g(x)) and exists read “f composed with g of x” or “f of g of x”.

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Answer:

Step-by-step explanation:

25 divide 77 = 0.32467532 x 100 = 32 (Leave off the rest, there is no such thing as a fraction of a person in this)

Simplified: (25/77)*100 = 32

To check our answer we would do 32 x 77%(.77) = 24.64 round-up and you get 25!

If you are still confused please do tell :)

According to the solving the length of the road in real life will be = 8 km.

The relationship (or ratio) between the distance on a map and the comparable distance on the ground is referred to as map scale. For example, on a 1:100000 scale map, 1cm on the map represents 1km on the ground.

You've probably seen maps with just a scale bar representing equal sections, each marked with kilometres or miles. These divisions have been used to calculate ground distance on a map. In other words, a map scale specifies the relationship between the map and indeed the entire or a portion of the earth's surface depicted on it.

scale on a map is 1 : 200,000.

= 1 : (200,000/(100*1000))

= 1:2

= 2km

So,

length of a road on the map is 4 cm.

= 4*2

= 8km

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The answer is 9cmsquare +5cmsquare equal to =106cm

Step-by-step explanation:

domain = (0,2)

range=(4,-4)

funcion =quadratic

Answer:

x= -6/5

Step-by-step explanation:

-2x=3x +6

collect like terms

-6=3x+2x

-6=5x

x= -6/5

Answer: x= -6/5 make that a fraction

decimal form: x= -1.2

mixed number form: x= - 1 1/5, 1 is the whole number

Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.

The amount they will expect to have in there account at the end of the investment is 44,440.71 dollars.

He grand parents wanted to invest in a bank.

They have $35,000 they are willing to invest for 6 years.

The interest rate is 4% and compounded quarterly.

The amount they will have in there account after 6 years can be calculated as follows:

using compound interest formula,

A = p(1 + r/n)ⁿᵇ

Where

Therefore,

p = 35000

r = 4% = 0.04

n = 4

b = 6

Amount = 35,000(1 + 0.04 / 4)⁴ˣ⁶

Amount = 35,000(1.01)²⁴

Amount = 35,000 × 1.26973464853

Amount = 44440.7126986

Amount = 44440.71 dollars

Therefore, the amount they will expect to have in there account at the end of the investment is 44,440.71 dollars.

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x = 3 and x = 6 is extraneous solution.

√(x+7) +5=x

Subtracting 5 on both sides of the equation

√(x+7) + 5 - 5 = x - 5

√(x+7) = x - 5

Squaring both sides of the equation

(√(x+7))² = (x - 5)²

x + 7 = x² + 25 - 10x

x² - 9x + 18 = 0 ...(1)

By middle term splitting equation (1) can be written as

x² - 6x - 3x + 18 = 0

x(x - 6) -3(x - 6) = 0

(x - 3)(x - 6) = 0

x - 3 = 0 and x - 6 = 0

x = 3, 6

Check extraneous solution by putting the value of x in the original equation, we get

Let x = 3

√(3+7) +5 = 3

✓10 + 5 = 3

which is a contradiction, so, x = 3 is an extraneous solution.

Let x = 6

√(6+7) +5 = 3

✓13 + 5 = 3

which is a contradiction, so, x = 6 is an extraneous solution.

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Answer:

3

Step-by-step explanation:

The greatest common divisor (GCD) of two nonzero integers a and b is the greatest positive integer d such that d is a divisor of both a and b (Wikipedia)

To find out which is the GCD of 72 and 159, keep factoring both until they cannot be factored any more

Then take the factors common to both list of factors; the greatest among them is the GCD

The factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

The factors of 159 are: 1, 3, 53, 159

The common factors are 1, 3

So GCD is 3

Answer: (10, 8)

Step-by-step explanation:

To solve a substitution question, you have to make sure either x or y is alone on the other side of equal sign.

-x + y = -2

^^^this becomes y = -2 + x

Now, since you know what "y" is, you simply replace "y" with our new equation in the other equation.

-x - 2(-2+x) = -26

Then, you do order of operations to get the answer.

First, do distributive property.

-x + 4 - 2x = -26

Next, solve the equation.

-3x + 4 = -26

-3x = -30

x = 10

Since you found what "x" is, you substitute "x" and in one of your equations to find "y", it doesn't matter which one.

-(10) + y = -2

-10 + y = -2

y = 8

Finally, after you got "x" which is 10, and "y" which is 8, you put them in an ordered pair (x, y) which is (10, 8).

P.S. I use Sora and Deltamath too!

Answer:

A and C

Step-by-step explanation:

Factors are numbers that can multiplied with another number to create a product. The factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56.

The solution of the equation which is as described in the task content when expressed in its simplest form is; -5/13.

It follows from the task content that the solution to the equation is to be determined and expressed in its simplest form.

Given;

-1/2 -1/2(4/5x+1) = -2 -3x

By distributing the coefficients: we have;

-1/2 - 2/5x - 1/2 = -2 -3x

Hence, by collecting like terms; we have;

-1/2 - 1/2 + 2 = -3x + (2/5)x

1 = -13x/5

Therefore; by cross-multiplication; we have;

5 = -13x

Divide both sides by; -13.

x = -5/13.

Ultimately, the solution of the equation which is as described in the task content when expressed in its simplest form is; -5/13.

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It is false that 2x + 7 = 3x + 1

The equations are given as

2x + 7 = 27

3x + 1 = 28

The above equations have different values

This means that

It is false that 2x + 7 = 3x + 1

The above statement is true because 27 does not equal 28

Hence, it is false that 2x + 7 = 3x + 1

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