Solve the proportion for b.
54
=
812
b = [?]

Answer:

width = 10 m

length = 16 m

Step-by-step explanation:

Formula

[tex]\textsf{Area of a rectangle} = wl[/tex]

[tex]\textsf{Perimeter of a rectangle}=2(w+l)[/tex]

(where  [tex]w[/tex] is width and [tex]l[/tex] is length)

Given:

Substituting the given values into the formulae to create two equations:

[tex]\textsf{Equation 1}: \quad wl=160[/tex]

[tex]\textsf{Equation 2}: \quad 2(w+l)=52[/tex]

Rearranging Equation 1 to make w the subject:

[tex]\implies w=\dfrac{160}{l}[/tex]

Substituting expression for w into Equation 2 and solving for [tex]l[/tex]:

[tex]\implies 2\left(\dfrac{160}{l}+l\right)=52[/tex]

[tex]\implies \dfrac{160}{l}+l=26[/tex]

[tex]\implies 160+l^2=26l[/tex]

[tex]\implies l^2-26l+160=0[/tex]

[tex]\implies l^2-10l-16l+160=0[/tex]

[tex]\implies l(l-10)-16(l-10)=0[/tex]

[tex]\implies (l-10)(l-16)=0[/tex]

[tex]\implies l=10, 16[/tex]

According to Equation 1:

As width < length, the dimensions of the shop are:

The value of x for each radical equation is 243 , 125,8,256 respectively.

The correct question is attached as an image with the answer.

When in an equation the variable is under a radical it is called a Radical Equation.

It is given in the question that

which radical matches to the solution

[tex]\rm \sqrt[5]{x^4} = 81 \\\\\sqrt[3]{x^4} = 625\\\\\sqrt[3]{x^5} = 32\\\\ \sqrt[4]{x^3}=64[/tex]

[tex]\rm x^4 = 81^5\\x = 243[/tex]

[tex]\rm x^4 = 625^3\\x = 125\\[/tex]

[tex]x^5 = 32^3\\x = 8\\[/tex]

[tex]\rm x ^3 = 64^4\\x = 256[/tex]

Therefore for each radical the value of x is determined.

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questions:you have been offered a scholarships to further your studies in Australia

write a diary entry sharing your experience about it

Answer:

17

Step-by-step explanation:

square root of x-1 +5=9

square root of x-1 = 4multiple by power of 2 because square root is cancled by 2.

x-1=16,x=17

Answer:

-4

Step-by-step explanation:

[tex]~~~~~-24 = 6x\\\\\\\implies -\dfrac{24} 6 = \dfrac{6x}6\\\\\\\implies x = -4[/tex]

Based on the calculations, the exact area of this rectangle is equal to 16√3 + 32 mm².

Mathematically, the area of a rectangle can be calculated by using this formula:

Area = Length × Width

Note: Radius (R) is equal to 2 mm.

Joining the center of the circles would form an equilateral triangle with side length of 2R. Also, the height of the equilateral triangle is given by:

Height = √2R² - R²

Height  = √3R

For the length and width of this rectangle, we have:

Length = R + 2R + R

Length  = 4R

Width = 2R + height of equilateral triangle

Width = 2R + √3R

Width = (2 + √3)R

Therefore, the area of a rectangle becomes:

Area = 4R × (2 + √3)R

Area = 4(2 + √3) × R²

Area = 4(2 + √3) × 2²

Area = (8 + 4√3) × 4

Area = 16√3 + 32 mm² ≡ a√3 + b

In conclusion, a = 16 and b = 32.

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Based on the definition of supplementary angles, the measure of both angles are: 80° and 100°.

The sum of angles that are supplementary to each other equals 180 degrees.

Let the measure of the supplementary angle be x.

The other angle will be: x + 20.

(x + 20) + x = 180

x + 20 + x = 180

2x + 20 = 180

2x = 180 - 20

2x = 160

x = 160/2

x = 80°

The other angle will be x + 20 = 80 + 20 = 100°.

The measure of the angles are: 80° and 100°.

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Answer:

yes

Step-by-step explanation:

yes, because there is a 99/1 chance. also, you can put 50 2010 coins in.

Answer:

Two lines are parallel if and only if they have the same slope.therefore the original line y=1/3x+2

so option 1 is the answer

A statement which best describes the function shown in the table is: B. exponential, there is a continual rate of decay or decrease.

An exponential function is a mathematical function whose numerical values (numerals) are generated by a constant that is raised to the power of an argument.

Given the following table:

X : -4        -1        2            4              5

Y :  16        2       0.25   0.0625    0.03125

Next, we would calculate the rate of decay for the y-values:

16/2 = 2/0.25 = 0.25/0.0625 = 0.0625/0.03125 = 8

Rule: The y-values constantly decreases by 1/4 or 0.25 of the previous number.

In conclusion, we can logically deduce that the function shown in the table is exponential, there is a continual rate of decay or decrease.

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Answer: It's B

Step-by-step explanation:

I got it right

The exact dimensions of the cone of largest volume that will fit inside the sphere will be 14.67 inches and 22✓2/3 inches.

From the information given, the height of the cone will be:

h = 11 + x

h = 11 + 3 2/3

h = 14 2/3 inches

The radius of the base of the cone will be:

= ✓121 - ✓121/9

= 2✓2(11)/3

= 22✓2/3

Therefore, the dimensions of the cone aren't 14.67 inches and 22✓2/3 inches.

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Answer:

24

Step-by-step explanation:

The interquartile range defines the difference between the third and the first quartile.

Let's put this data set in ascending order:

24, 36, 48, 52, 52, 60, 72

The median is 52. The median of both the lower (1st quartile) and upper half (3rd quartile) of the data is 36 and 60.

Now we can subtract the first quartile from the third quartile (60 - 36) to get the interquartile range of 24.

Hope this helped! :)

The correct answer is option C which is 3 sets of 2 negative tiles.

Multiplication is the process of determining the product of two or more numbers in mathematics.

We have the product of 3 and -2. We can represent this as 3 is equivalent to -2 negative tiles.

When we add -2 three times -2 - 2 -2 = -6 we will get -6 that is 3 sets of 2 negative tiles.

So when we multiply it by 3, we end with 3 sets of 2 negative tiles. This is because the order of the factors does not change the product.

Therefore the correct answer is option C which is 3 sets of 2 negative tiles.

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The length of the fencing needed for the dog run will be 76 feet

The measure of the size of any object or the distance between the two endpoints will be termed the length.

Given that:-

Area of Dog Run = 240

Length of Dog Run = 30

The solution will be done as below:-

Width of Dog Run = 30 - x

Area of Dog Run:  30 * (30 - x) = 240

240 / 30 = 30 - x

8 = 30 - x

x = 24

Width of Dog Run = 8

How many feet of fencing will George need for the dog run?

Perimeter of Dog Run = 2Length + 2Width

Perimeter of Dog Run = (2 * 30) + (2 * 8)

Perimeter of Dog Run = 60 + 16

The perimeter of Dog Run = 76

Therefore the length of the fencing needed for the dog run will be 76 feet

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Answer:

C. 76 feet

Step-by-step explanation:

windows

Answer:

Concave octagon

Step-by-step explanation:

Concave octagon:

So, this is a concave octagon

[tex]~~(2I_2)A\\\\\\=2\begin{bmatrix} 1&0\\0&1 \end{bmatrix}\begin{bmatrix} 4&2\\3&-3 \end{bmatrix}\\\\\\=\begin{bmatrix} 2&0\\0&2 \end{bmatrix}\begin{bmatrix} 4&2\\3&-3 \end{bmatrix}\\\\\\=\begin{bmatrix} 8+0&4+0\\0+6&0-6 \end{bmatrix}\\\\\\=\begin{bmatrix} 8&4\\6&-6 \end{bmatrix}[/tex]

Answer:

b

Step-by-step explanation:

Amount of tax you need to pay on a taxable income of $40,000 is,

= $6423.75

It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.

According to table, $40,000 falls in the 3rd category between $31,850 and $77,100

And, The tax is "$4,386.25 + 25% of amount over 31,850"

Hence, we have:

= $4,386.25 + 25% of (40,000 - 31,850).

= $4,386.25 + 0.25 x 8150

= $6423.75

Thus, Amount of tax you need to pay on a taxable income of $40,000 is,

= $6423.75

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Answer:

1/9x

Step-by-step explanation:

The parenthesis around the 9x means that the -1 exponent goes to the whole thing (the 9x) To "fix" a negative exponent push the 9x across a fraction bar to make the exponent positive. When you push the 9x down across a fraction bar that leaves a 1 on top of the fraction, that has nothing to do with the 1 exponent. Its a 1 on top because when you push the 9x down there is nothing left on top so it is a 1.

(9x)^-1

= 1/9x

To be clear, this is a 1 one top and a 9x on the bottom of a fraction.

The value of x and y is -0.0434 and -4.5652.

equation, statement of equality between two expressions consisting of variables and/or numbers.

given:

x - 4.5y=20.5

x + 4.7y= -21.5

Solving above two equation we have:

20.5+4.5y=-21.5-4.7y

42= -9.2y

y= -42/9.2

y= -4.5652

x=-0.0434

Hence, the value of x and y is -0.0434 and -4.5652.

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Answer:

Top right graph

Step-by-step explanation:

Graph is in attached image.

Answer:

hence the answer for given problem is -2, but andrew get -21.6 which is wrong

Step-by-step explanation:

The solution of the fraction 5/8 +3/4 over -2/3 - 5/6 is -11/12

5/8 + 3/4 ÷ -2/3 - 5/6

(5+6) / 8 ÷ (-4-5) / 6

= 11/8 ÷ -9/6

= 11/8 ÷ -3/2

= 11/8 × 2/-3

= 22/-24

= -11/12

Therefore, the solution of the fraction 5/8 +3/4 over -2/3 - 5/6 is -11/12

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The rate of each train of the northbound train traveled 10 miles per hour faster than the southbound train 26 miles per hour.

Speed is the time rate at which an object is moving along a path

Let the speed of southbound train is x miles/hour

so, northbound train has speed of x+10 miles/hour.

then, Speed of both train = Total distance/ total time

(x+10+x)=210/5

2x+10= 210/5

2x+10= 42

2x= 32

x= 16 miles per hour (southbound train)

northbound train:  16+10=26 miles per hour

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Answer:

Step-by-step explanation:

Let that be theta

Here perpendicular is lamp post and base is the shadow

Answer:

59.0° (nearest tenth)

Step-by-step explanation:

This can be modeled as a right triangle (see attachment).

To find the angle of elevation (marked as [tex]x[/tex] on the attached diagram), use the tan trig ratio:

Tan trigonometric ratio

[tex]\sf\tan(\theta)=\dfrac{O}{A}[/tex]

where:

Given:

Substitute the given values into the formula and solve for x:

[tex]\implies \sf\tan(\theta)=\dfrac{10}{6}[/tex]

[tex]\implies \sf\theta=\tan^{-1}\left(\dfrac{10}{6}\right)[/tex]

[tex]\implies \theta = \sf 59.03624...^{\circ}[/tex]

[tex]\implies \theta = \sf 59.0^{\circ}\:(nearest\:tenth)[/tex]

Answer:

If the cost of 3 notebooks is 30.30, we can infer the cost of one notebook is 10.10.

Step-by-step explanation:

[tex]10.10 * 15 = x[/tex]

[tex]10.10 * 15 = 151.5[/tex]

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to find the cost of 15 notebooks, given that the cost of 3 notebooks is 30.30.

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

So we divide the cost of three notebooks (30.30) by 3:

[tex]\star~\large\pmb{30.30\div3}[/tex]

[tex]\star~\large\pmb{10.10}[/tex]

That's the cost of 1 notebook. Now, multiply that times 15 (we're asked to find the cost of 15 notebooks).

[tex]\star~\large\pmb{10.10\times15}[/tex]

This gives us:

[tex]\star~\large\pmb{151.5}[/tex]

That's the cost of 15 notebooks if the cost of one notebook is 10.10.

Hope it helps you out! :D

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Answer:

[tex] \frac{7}{2} [/tex]

Step-by-step explanation:

[tex] \frac{3! + 0!}{2! \times1! } = \frac{(3 \times 2 \times 1) + 1}{(2 \times 1) \times 1} = \frac{6 + 1}{2} = \frac{7}{2} [/tex]

Answer: 29, 31, 37, 41, 43, 47, 53.

Step-by-step explanation: