A rectangular room is twice as long as its breadth and its perimeter is 48 m. Find the cost of carpeting its floor at Rs. 75 per sq.m. ​

9514 1404 393

Answer:

  (x, y) = (59/45, 11/15) ≈ (1.311, 0.733)

Step-by-step explanation:

A graphing calculator shows us the solution is not integer values, so we may find it easiest to solve these equations using the "cross-multiplication method."

Writing the equations in general form, we have ...

  3x -4y -1 = 0

  6x +7y -13 = 0

Then we can form an array of the coefficients, repeating the first column:

  [tex]\begin{array}{cccc}3&-4&-1&3\\6&7&-13&6\end{array}[/tex]

Forming differences of cross products involving adjacent pairs of columns gives ...

  d1 = (3)(7) -(6)(-4) = 45

  d2 = (-4)(-13) -(7)(-1) = 59

  d3 = (-1)(6) -(-13)(3) = 33

Then the solutions are found from ...

  1/d1 = x/d2 = y/d3

or

  x = d2/d1 = 59/45

  y = d3/d1 = 33/45 = 11/15

The solution is (x, y) = (59/45, 11/15) ≈ (1.311, 0.733).

_____

Additional comment

This takes longer to explain than to do. One reason we like it is that the number of math operations is slightly smaller than the number of math operations required for substitution or elimination. It is especially nice when the solution is not a pair of integers.

Answer:

12.57 in⠀⠀⠀⠀⠀

Answer:

12.56 inches

Step-by-step explanation:

A= pie x r^2

= 3.14 × 2^2

= 3.14 × 4

= 12.56

Answer:

10, 100, 1,000, 10,000, 100,000

If you are adding one zero in the end for every number, then 100,000 will be your next number

Answer

8,98

Step-by-step explanation:

the minimum amount of weight you can use is the barbell alone which is 8lbs by itself and the maximum is 98 because there are 6 15lb plates which equal to 90lb total and when you add the 6 plates to the barbell you get 98lbs

Answer:

1/2 chance

Step-by-step explanation:

5 and 10 can be divided down to 1/2

exercise 1

1) 12 000 : 1,33 = 9022,55 €

exercise 2

1) 9200 : x = 100% : 2%

  (9200*2) : 100 = 184 rupees

(sorry dont know the other two ones)

[tex]\huge\color{purple}\boxed{\colorbox{black}{♡Solution♡}}[/tex]

[tex]8 \: {m}^{2} - 5 \: m + 1[/tex] ✅

Step-by-step explanation:

[tex] \frac{(16 \: {m}^{3} - 10 \: {m}^{2} + \: 2m) }{2 \: m} \\ \\ = \frac {2 \: m \: (8 \: {m}^{2} - 5 \: m + 1)} {2 \: m} \\ \\ = 8 \: {m}^{2} - 5 \: m + 1[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}[/tex]

Answer:

I don't know what the answer choices are because this question is used twice But if im guessing correctly you mean the one where the answer choices are 6, 8, 12, and 24. The Correct answer is 6

a2 + 8a + 12 = (a + 2)(a + )

The answer is 6

Step-by-step explanation:

Answer:

sinx= d/f

cosx= e/f

tanx= d/e

Answer: 2,396,558 Ringgit

Step-by-step explanation:

J = P * ( 1 + k)^n

P = initial investment of 1,000,000 Ringgit

k = rate of return of 6% per annum

n = Number of years of investment

J = 1,000,000 * ( 1 + 6%)¹⁵

= 1,000,000 * 2.396558193

= 2,396,558 Ringgit

Answer:

Area of circle bounded by a 135 ° arc is 4.71 m ²

Step-by-step explanation:

Radius of circle, r = 2 m

Angle of the circle , θ = 135 °

Area of circle bounded by a 135 ° arc.

Using Formula

Area of circle = θ/ 360 × π × r ²

substitute the values,

Area of circle = 135 /360 × 3.14 × ( 2 m) ²

solve it

Area = 27 / 72 × 3.14 × 4 m ²

Area = 27 / 18 × 3.14

Area = 1.5 × 3.14

Area = 4.71 m ²

Therefore, Area of circle bounded by a 135 ° arc is 4.71 m ²

Answer:

it's 3/2pi

Step-by-step explanation:

.

Answer:

C)

Step-by-step explanation:

[tex]2xy^{2}-5y^{5}[/tex]

Binomial should have two terms. Five degree binomial means highest degree of the binomial should be 5

Answer:

four minus three

Step-by-step explanation:

your welcome

4) Let the number be : N

Given : 10% of this number is 25

[tex]\sf{\implies 10\% \ of \ N = 25}[/tex]

[tex]\sf{\implies \dfrac{10}{100} \times N = 25}[/tex]

[tex]\sf{\implies \dfrac{N}{10} = 25}[/tex]

[tex]\sf{\implies N = 250}[/tex]

Now we need to find 60% of 250

[tex]\sf{\implies \dfrac{60}{100} \times 250}[/tex]

[tex]\sf{\implies 6 \times 25}[/tex]

[tex]\sf{\implies 150}[/tex]

5) Given : James left the home at 10 : 00 AM

First : He will meet his friend Tom at the skate park which is 15 minutes walk from his home.

So, James reached the skate park 10 : 15 AM

Second : They stayed at the skate park for an hour

So, till 11 : 15 AM James and Tom were at skate park

Third : Then they will take a 10 minutes walk over to the Burger bar

So, James and Tom reached the Burger bar at 11 : 25 AM

6) First let us find 75% of 80

[tex]\sf{\implies \dfrac{75}{100} \times 80}[/tex]

[tex]\sf{\implies 15 \times 4}[/tex]

[tex]\sf{\implies 60}[/tex]

Now let us find 40% of 30

[tex]\sf{\implies \dfrac{40}{100} \times 30}[/tex]

[tex]\sf{\implies 12}[/tex]

Now, (60 - 12) = 48

Answer: 75% of 80 is 48 greater than 40% of 30

7) Given : Journey to school takes 70 minutes

We know that : 1 hour = 60 minutes

So, 70 minutes = 1 hour + 10 minutes

Given : Boy leaves the home at 0715

Answer: The Boy arrives at 0825

Answer:

option A

Step-by-step explanation:

[tex]\frac{x^a}{x^b} = x^{a-b}[/tex] , [tex]z^0 = 1[/tex]

So,

[tex]\frac{18x^5 y}{6xy^8z^0} = \frac{18}{6} \times x^{5 -1} \times y^{1-8} = 3 x^4 \times y^{-7} = \frac{3x^4}{y^7}[/tex]

=====================================

Work Shown:

area = base*height

area = 16*7

area = 112 square cm

----------------

Extra info (optional section):

The area formula for a parallelogram is the same as the formula for a rectangle. Imagine tilting a rectangle so that it's slanted. The area has not changed.

Or another thing to imagine is that let's say we had a stack of 2 by 4s. If the stack is perfectly vertical, aka forming a rectangle, then we can nudge the beams so that we can form a slanted parallelogram instead. Both configurations involve the same amount of wood, and therefore would lead to the same frontal surface area.

Answer:

not a answer

Step-by-step explanation:

try using demos graphing calculator

Answer:

(-2,-5)

Step-by-step explanation:

Y=x^2/2 +2x-3

Y=1/2 ×(x+2)^2 -5

a=1/2

h=-2

k=-5

(-2,-5)

The requried vertex of the parabola y = (1/2)x² + 2x - 3 is (-2, -5).

A parabola is a cross-section cut out of the cone and represented by an equation y = 4ax².

To find the vertex of the parabola defined by the equation y = (1/2)x² + 2x - 3, we can use the fact that the vertex is located at the point (-b/2a, f(-b/2a)), where a and b are the coefficients of the quadratic term and the linear term, respectively.

In this case, a = 1/2 and b = 2, so we can substitute these values into the formula to get:

x-coordinate of vertex = -b/2a = -2/(2*1/2) = -2

To find the y-coordinate of the vertex, we can substitute this value of x into the equation and simplify:

y-coordinate of vertex = (1/2)(-2)² + 2(-2) - 3

= 1/2(4) - 4 - 3

= -5

Therefore, the vertex of the parabola y = (1/2)x² + 2x - 3 is (-2, -5).

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Answer:

Step-by-step explanation:

The line is parallel to the x axis, so its slope is 0

m = 0

the y intercept is -2.5

the line doesn’t intercept the x axis because is parallel to it

Answer:

Step-by-step explanation:

1). Step 4:

   [tex]x=5^{\frac{4}{3}}=(5^4)^{\frac{1}{3}}[/tex]

   [tex]x=\sqrt[3]{5^4}[/tex] [Since, [tex]a^{\frac{1}{3}}=\sqrt[3]{a}[/tex]]

   [tex]x=\sqrt[3]{5\times 5\times 5\times 5}[/tex]

   Step 5:

   [tex]x=\sqrt[3]{(5)^3\times 5}[/tex]

   [tex]x=\sqrt[3]{5^3}\times \sqrt[3]{5}[/tex]

2). He simplified the expression by removing exponents from the given expression.

3). Let the radical equation is,

   [tex](3x-1)^{\frac{1}{5}}=2[/tex]

   Step 1:

   [tex](3x-1)^{\frac{1}{5}\times \frac{5}{1} }=2^{\frac{5}{1}}[/tex]

   Step 2:

   [tex](3x-1)=2^5[/tex]

   Step 3:

   [tex]3x=32+1[/tex]

   Step 4:

   [tex]x=11[/tex]

4). By substituting [tex]x=11[/tex] in the original equation.

   [tex](3\times 11-1)^{\frac{1}{5}}=(32)^\frac{1}{5}[/tex]

                         [tex]=(2^5)^\frac{1}{5}[/tex]

                         [tex]=2[/tex]

There is no extraneous solution.

1). Step 4:

   x=5^{\frac{4}{3}}=(5^4)^{\frac{1}{3}}x=534=(54)31

   x=\sqrt[3]{5^4}x=354 [Since, a^{\frac{1}{3}}=\sqrt[3]{a}a31=3a

   x=\sqrt[3]{5\times 5\times 5\times 5}x=35×5×5×5

   Step 5:

   x=\sqrt[3]{(5)^3\times 5}x=3(5)3×5

   x=\sqrt[3]{5^3}\times \sqrt[3]{5}x=353×35

2). He simplified the expression by removing exponents from the given expression.

3). Let the radical equation is,

   (3x-1)^{\frac{1}{5}}=2(3x−1)51=2

   Step 1:

   (3x-1)^{\frac{1}{5}\times \frac{5}{1} }=2^{\frac{5}{1}}(3x−1)51×15=215

   Step 2:

   (3x-1)=2^5(3x−1)=25

   Step 3:

   3x=32+13x=32+1

   Step 4:

   x=11x=11

4). By substituting x=11x=11 in the original equation.

   (3\times 11-1)^{\frac{1}{5}}=(32)^\frac{1}{5}(3×11−1)51=(32)51

                         =(2^5)^\frac{1}{5}=(25)51

                         =2=2

There is no extraneous solution.

Answer: A. Long-term capital gains are from investments that have been held for more than one year and are taxed at a lower rate than short-term capital gains.

Step-by-step explanation:

Long-term capital gains are indeed from investments that have been held for more than a year as opposed to short term gains from investments of less than a year. This means that long term gains can come from investments such as stocks and bonds.

Long-term capital gains are taxed at a lower rate than short term gains with most long term gains being taxed at 15% or lower. This is in contrast to short-term gains that are taxed at the same rate as ordinary income which means it could go up to as high as 37%.

Answer: A

Step-by-step explanation:

Answer:

He should measure the length of the bowling alley using meters

Step-by-step explanation:

The score does Tyrone need in the fifth game so that his mean score is 125 is 168.

It is defined as the sum of all observations divided by the number of observations.

Given

Tyrone's bowling scores for the first four games of the season were 120,123,105, and 109. He wants to increase his mean score to 125.

[tex]\frac{120+123+105+109+x}{4+1} =125[/tex]

⇒ [tex]\frac{457+x}{4+1} =125[/tex]

⇒ [tex]\frac{457+x}{5} =125[/tex]

⇒ [tex]{457+x} =125[/tex] × [tex]5[/tex]

⇒ [tex]{457+x} =625[/tex]

⇒ [tex]x =625-457[/tex]

⇒ [tex]x =168[/tex]

Hence, the score does Tyrone need in the fifth game so that his mean score is 125 is 168.

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Answer:

in all cases x/100 is just a way to represent percentage. and since it's the same everywhere, it's not even relevant to decide wich option describes the context right

A) 80/140 is the portion that describes the book readers over all people surveyed

B) 31/63 just 63 people are relevant bc it's specified that we only consider beach travelers.

that also explains the 31, bc that's the number of beach travelers who'd like to watch a movie

C) 15/80 only 80 movie watchers in total, of whom 15 would prefer the city

Answer:

1/12 of the lasagna was left

Step-by-step explanation:

To find out how much of the lasagna has been eaten, you have to find the least common denominator (LCD) for the three fractions. The LCD of 1/3, 1/4, and 1/6 is 12 (3x4x6). Now convert all the fractions so that all of their denominators is equal to 72 (1/3=4/12, 1/4=3/12, 1/6=2/12), then add all of the fractions together (4/12 + 3/12 +2/12 = 3/4). 3/4 of the lasagna has been eaten and the remaining lasagna is 1/12 (1-3/4=4/4-3/4).

Answer:

[tex]\frac{1}{4}[/tex] of the lasagna

Step-by-step explanation:

[tex]\frac{1}{4} +\frac{1}{6}+ \frac{1}{3}[/tex]

4 = 2 × 2

3 = 3

6 = 2 × 3

LCM = 2 × 2 × 3

LCM = 12

4 × 3 × 6 = 72

[tex]\frac{18}{72} +\frac{12}{72}+ \frac{24}{72}[/tex]

[tex]\frac{18+12+24}{72}[/tex]

[tex]\frac{54}{72}[/tex]

54 = 2 × 3 × 3 × 3

72 = 2 × 2 × 2 × 3 × 3

GCF = 2 × 3 × 3

GCF = 18

[tex]\frac{\frac{54}{18} }{\frac{72}{18} }=\frac{3}{4}[/tex]

[tex]1-\frac{3}{4}[/tex]

[tex]\frac{4}{4} -\frac{3}{4}[/tex]

[tex]\frac{4}{4} -\frac{3}{4}=\frac{1}{4}[/tex]

Answer:

35/2 or 17.5

Step-by-step explanation:

2x / 7 - 3 = 2

2x / 7 - 3 + 3 = 2 + 3

2x / 7 = 5

(2x /7) x 7 = 5 x 7

2x = 35

x = 35/2 or 17.5

Answer:

[tex]x = \frac{35}{2} [/tex]

Step-by-step explanation:

[tex] \frac{2x}{7} -3=2[/tex]

[tex] \frac{2x}{7} = 2 + 3[/tex]

[tex]\frac{2x}{7} = 5[/tex]

[tex]x = \frac{7}{2} \times 5[/tex]

[tex]x = \frac{35}{2} [/tex]

Decimal Form:

[tex]x = 17.5[/tex]

Mixed Number Form:

[tex]x = 17 \frac{1}{2} [/tex]