The four walls of a room including the doors and windows have to be painted.

The dimensions of the room are 5m x 5m x 6 m. Find the area to be painted.​

The interest rate for an investment to quadruple after 7 years of continuous compound interest would be = 57%

Continuous compound interest is defined as the type of interest that is accumulated overtime which is related to an investment made for a period of time.

The number of years = 7 years

simple interest = 1

Rate = X

But 100/7 = X

X4 = 100/7×4

X = 400/7

X= 57%.

Therefore, to receive a quadruple investment after 7 years, the rate would be at 57% .

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19.80

Step-by-step explanation:

Answer:

the answer will be 117

Step-by-step explanation:

you need to multiply

The interest is 16% compounded semi-annually, is Rs. 121,179.10.

To determine how much money needs to be deposited now to provide a payment of Rs. 15,000 at the end of each half year for 10 years, we will use the formula for the present value of an annuity.

Present value of an annuity = (Payment amount x (1 - (1 + r)^-n))/rWhere:r = interest rate per compounding periodn = number of compounding periodsPayment amount = Rs. 15,000n = 10 x 2 = 20 (since there are 2 half years in a year and the payments are made for 10 years)

So, we have:r = 16%/2 = 8% (since the interest is compounded semi-annually)Payment amount = Rs. 15,000Using the above formula, we can calculate the present value of the annuity as follows:

Present value of annuity = (15000 x (1 - (1 + 0.08)^-20))/0.08 = Rs. 121,179.10Therefore, the amount that needs to be deposited now to provide payment of Rs. 15,000 at the end of each half year for 10 years, if the interest is 16% compounded semi-annually, is Rs. 121,179.10.

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Wash would pay R320.85 per month, including VAT, if they use 25 kl of water.

What is percentage ?

To calculate how much Mr. Msiza's car wash pays a month including VAT when they use 25 kl of water, we need to determine which block(s) the usage falls into and calculate the total charge.

The usage of 25 kl falls into block 3, which has a charge of R11.16 per kilolitre (excluding VAT).

The total charge for 25 kl of water, including VAT at a rate of 15%, is:

25 kl x R11.16/kl = R279.00 (excluding VAT)

VAT = 15% x R279.00 = R41.85

Total charge including VAT = R279.00 + R41.85 = R320.85

Therefore, Mr. Msiza's car wash would pay R320.85 per month, including VAT, if they use 25 kl of water.

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The error that the manager made was that B. The manager divided 5/4 by 16 instead of dividing 4/5 by 16.

The information illustrates that the project manager is calculating work forecasts and he manager's team completed 4/5 of a job in 16 days.

Therefore, the amount that was done each day will be:

= 4/5 ÷ 16

= 4/5 × 1/16

= 4/80

= 1/20

Therefore, the error that the manager made was that the manager divided 5/4 by 16 instead of dividing 4/5 by 16. This was the reason that he got 5/64.

Therefore, the correct option is B.

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Answer:

6/5=x/15

Step-by-step explanation:

6/5=x/15,where x is hight of the lamp post

x=18

Answer:

if f(x)=2x+1 then insert 6 in x

f(6)=2*6+1

f(6)=13

so the answer is 13

Answer:

-8/15

Step-by-step explanation:

Divide the fraction

Answer:

8/15

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

The rules for change of coordinates are:

r = √(x^2 + y^2)

θ = tan(y/x)

and:

x = r*cos(θ)

y = r*sin(θ)

1) Now we have the equation:

r = (9/7)*cos(θ) + 2*sin(θ)

Let's multiply both sides by r:

r^2 = r*(  (9/7)*cos(θ) + 2*sin(θ) )

r^2 = (9/7)*r*cos(θ) + 2*r*sin(θ)

Now we can replace:

r*cos(θ) by x and r*sin(θ) by y

r^2 = (9/7)*x + 2*y

And we know that:

r = √(x^2 + y^2)

then:

r^2 = x^2 + y^2

So we can replace that in our equation:

x^2 + y^2 = (9/7)*x + 2*y

This is the equation in cartesian coordinates.

2) Now we want to describe the curve.

We can rewrite this as:

[x^2  - (9/7)*x] + [ y^2 - 2*y] = 0

Now we can complete squares:

So we need to add and subtract:

(4.5/7)^2 and 1^2

[x^2  - 2*(4.5/7)*x + (4.5/7)^2 -  (4.5/7)^2] + [ y^2 - 2*y + 1 - 1]  = 0

(x - (4.5/7) )^2 + (y - 1)^2   - 1 - (4.5/7) = 0

(x - (4.5/7) )^2 + (y - 1)^2  = 1 + 4.5/7

So this is the equation of a circle, centered at:

( 4.5/7, 1) and with a radius √(1 + 4.5/7)

Answer:

3 cups of sugar

Step-by-step explanation:

you increase it as per ratio,in this case ratio is 1.5

Answer:

The table should measure diagonally about 41.23 inches.

Step-by-step explanation:

To find the diagonal of a rectangle we use the formula :

\(a^{2}\) + \(b^{2}\) = \(c^{2}\)

A and B both represent the side lengths of the rectangle, while C is the diagonal part. Knowing this formula, let's plug in the values for A and B and see what happens.

\(32^{2}\) + \(26^{2}\) = \(c^{2}\)

1024 + 676 = \(c^{2}\)

1700 = \(c^{2}\)

The square root of 1700 is (rounded to the hundreth's place) = 41.23

Answer:

c41

Step-by-step explanation:

The value of ( i )³⁸ will be equal to -1. The correct option is B.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given expression ( i )³⁸ is the I value of the complex number. The I value of the complex number is equal to the square root of the negative one. The expression will be solved as below:-

( i )³⁸ = (√-1)³⁸

( i )³⁸ = -1

Therefore, the value of ( i )³⁸ will be equal to -1. The correct option is B.

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Answer:

11.75

Step-by-step explanation:

141/12=11.75 simply math dudette

Answer:

i believe it is the second one.

Step-by-step explanation:

hope this helps! pls mark as brainliest!

Answer:

the second is the answer

Step-by-step explanation:

98-98+g = 150-98

= 52

Answer:

The answer is Ahope this helps

Answer:

24 : 15 : 20

Step-by-step explanation:

express ratios in fractional form and express b and c in terms of a

\(\frac{a}{b}\) = \(\frac{8}{5}\) ( cross- multiply )

8b = 5a ( divide both sides by 8 )

b = \(\frac{5}{8}\) a

also

\(\frac{b}{c}\) = \(\frac{3}{4}\) ( cross- multiply )

3c = 4b ( divide both sides by 3 )

c = \(\frac{4}{3}\) b = \(\frac{4}{3}\) × \(\frac{5}{8}\) a = \(\frac{5}{6}\) a

Then

a : b : c

= a : \(\frac{5}{8}\) a : \(\frac{5}{6}\) a ( multiply each part by 24, the LCM of 8 and 6 )

= 24a : 15a : 20a ( divide each part by a )

= 24 : 15 : 20 ← in simplest form

Answer:

Proofs provided below

Step-by-step explanation:

\(\bold {\text{Prove } (a + b)^2 = a^2 + 2ab + b^2}}\)

\(\\\\\implies (a + b)^2 = (a+b) \times (a+b)\\\\\implies (a + b)^2 = a \times (a+b) +b \times (a+b)\\\\\implies (a + b)^2 = a \times a + a \times b + b \times a + b \times b\\\\\implies (a + b)^2 = a^2+ab+ba+b^2\\\\\implies (a + b)^2 = a^2+ab+ab+b^2 \;\;\;\;\text{ since ab = ba}\\\\\implies (a+b)^2 = a^2+2ab+b^2\\\\\)

\(\bold{\text{Prove } a^2-b^2 \,=\, (a+b)(a-b)\\\\}\)

1. Add and subtract ab to LHS
\(\implies a^2-b^2 = a^2-b^2-ab+ab\\\\\implies a^2-b^2 = a^2-ab+ab-b^2\\\\\)

2. Factorize the above expression
\(\implies a^2-b^2 = a(a-b)+b(a-b)\\\\\implies a^2-b^2 = (a-b)(a+b) \;\;\;\; \text{since (a-b) is a common factor in RHS }\)

∴  (a² - b²) = (a - b) (a + b)

\(\bold{\text{Prove $\dfrac{\sqrt{3}+1}{\sqrt{3}-1}$= $2+\sqrt{\ensuremath{3}}$}}\\\)

\(\text{1. Multiply LHS by $\dfrac{\sqrt{\text{}3}-1}{\sqrt{3}-1}$}\\\\\implies $\dfrac{\sqrt{\text{}3}+1}{\sqrt{3}-1}$ \times $\dfrac{\sqrt{\text{}3}-1}{\sqrt{3}-1}$ \\\\\)

\(\implies \dfrac{ (\sqrt{3} + 1)(\sqrt{3}-1) }{(\sqrt{3} - 1)(\sqrt{3}-1) }\\\\\)

Numerator is
\((\sqrt{3} + 1)(\sqrt{3}-1) = (\sqrt{3})^2 - 1^2 = 3 - 1 = 2\\\\\)

Denominator is
\((\sqrt{3}-1)^2 = (\sqrt{3})^2 - 2\cdot \sqrt{3} \;\cdot 1 + (-1)^2\\\\= 3 - 2 \sqrt{3} + 1\\\\= 4 - 2 \sqrt{3}\\\\\)

So LHS becomes
\(\dfrac{2}{4 - 2\sqrt{3}} \\\\\)

Dividing numerator and denominator by 2 yields

\(\dfrac{2}{4 - 2\sqrt{3}} = \dfrac {1}{2 - \sqrt{3}}\)

Multiply numerator and denominator by \({2-\sqrt {3}}\)

\($\dfrac{1\cdot(2+\sqrt{3})}{(2-\sqrt{3})(2+\sqrt{3)}}$\)

\(=$\dfrac{\ensuremath{2}+\sqrt{3}}{2^{2}-(\sqrt{3)^{2}}}=$$\dfrac{\ensuremath{\ensuremath{2}+\sqrt{3}}}{4-3}=\ensuremath{2}+\sqrt{3}$\)

Hence Proved

Answer:

The slope of the tangent line to the curve at the given point is -11/7.

Step-by-step explanation:

Differentiation is an algebraic process that finds the gradient (slope) of a curve.  At a point, the gradient of a curve is the same as the gradient of the tangent line to the curve at that point.

Given function:

\(4x^2+5xy+y^4=370\)

To differentiate an equation that contains a mixture of x and y terms, use implicit differentiation.

Begin by placing d/dx in front of each term of the equation:

\(\dfrac{\text{d}}{\text{d}x}4x^2+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=\dfrac{\text{d}}{\text{d}x}370\)

Differentiate the terms in x only (and constant terms):

\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=0\)

Use the chain rule to differentiate terms in y only. In practice, this means differentiate with respect to y, and place dy/dx at the end:

\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

Use the product rule to differentiate terms in both x and y.

\(\boxed{\dfrac{\text{d}}{\text{d}x}u(x)v(y)=u(x)\dfrac{\text{d}}{\text{d}x}v(y)+v(y)\dfrac{\text{d}}{\text{d}x}u(x)}\)

\(\implies 8x+\left(5x\dfrac{\text{d}}{\text{d}x}y+y\dfrac{\text{d}}{\text{d}x}5x\right)+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

\(\implies 8x+5x\dfrac{\text{d}y}{\text{d}x}+5y+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

Rearrange the resulting equation in x, y and dy/dx to make dy/dx the subject:

\(\implies 5x\dfrac{\text{d}y}{\text{d}x}+4y^3\dfrac{\text{d}y}{\text{d}x}=-8x-5y\)

\(\implies \dfrac{\text{d}y}{\text{d}x}(5x+4y^3)=-8x-5y\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8x-5y}{5x+4y^3}\)

To find the slope of the tangent line at the point (-9, -1), substitute x = -9 and y = -1 into the differentiated equation:

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8(-9)-5(-1)}{5(-9)+4(-1)^3}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{72+5}{-45-4}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{77}{49}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{11}{7}\)

Therefore, slope of the tangent line to the curve at the given point is -11/7.

Answer:

True

Step-by-step explanation:

I hope this is correct and have a great day

Answer:

True

Step-by-step explanation:

People save receipts to keep track of their previous purchases and expenses.

I hope this helps

Answer:

Provided an explanation below.

The examples are not asking you to solve, only to simplify the expression

For the examples you posted, not sure if you want the solutions are not; I have gone ahead and simplified

\(1.\; -8x^3y^5\\\\2\; \dfrac{2y^3}{3}\\\\3.\; They are both equal\\\\4.\; 3x^2\\\\\)

Step-by-step explanation:

First let's understand what an exponent is.

When a number or a term or an expression is multiplied repeatedly by itself, an exponent can be used to represent this situation

for example,

5 x 5 x 5 x 5 x 5 x 5 = 5⁶ since 5 is multiplied by itself 6 times

Here the number being multiplied(5) is called the base and the number of times it is multiplied(6) is called the exponent.

There are some rules regarding exponentiation

1 Zero Exponent

Any number raised to the power zero is 1

\(4^0 = 1\\\\123.456^0 = 1\\\\x^0 = 1\)

2. Negative Exponent
If the exponent if negative, the expression is equivalent to the reciprocal of the term raised to the positive exponent

In general

\(a^{-m} = \dfrac{1}{a^m}\\\\and\\\\\dfrac{1}{a^{-m}} = a^m\\\\\)

Examples:

\(x^-1 = \dfrac{1}{x}\\\\\left({x + y}\right)^{-a} = \dfrac{1}{(x+y)^a}\)  

\(\dfrac{1}{x^{-3}} = x^3\)

3. Product Rule
When you multiply exponents with the same base the exponents get added

In general
\(\displaystyle {a^m a^n = a^{m + n}}\)

Examples

\(x^3x^6 = x^{(3+6)} = x^9\\\\\)

4. Quotient Rule

When you divide an exponentiated term by another exponentiated term with the same base the resulting exponent is the difference between the two exponents:

In general

\(\dfrac{a^m}{a^n} = a^{m-n\)

Examples

\(\dfrac{y^3}{y^2} = y^{3-2} = y^1 = y\)

5. Power Rule 1

An exponent term raised to another power will be the base raised to the product of the two exponents

In general

\((a^m)^n = a^{mn}\)

\((x^3)^4 = x^{3 \cdot 4} = x^{12}\)

6. Power Rule 2

If the base is the product of two or more terms and the whole expression is raised to a power then each individual term gets raised to that power.

\((ab)^m = a^mb^m\\\\(2x^3y^2z^4)^4 = 2^4x^{3.4}y^{2.4}z^{4.4} = 16x^{12}y^8z^{16}\)

7. One exponent
Any term raised to the power 1 is itself
\(a^1 = a\)

example: 5¹ = 5

x¹ = x

You may have to use some or all of the rules when confronted with a specific problem

There are plenty of excellent resources on the web which can explain far more lucidly than I can.

Here are a few. Just search for them and you will get the site links
LibreTexts, OpenStax, cK-12.org etc

As for the specific examples you posted:

\(1. (4xy^2)(-2x^2y3)\\\)

 \(\textrm{2. }\dfrac{6y^2}{18x}\cdot 2xy\)

3. Which expression has the greater value?
\(2^3.2^5 \; or\; \dfrac{4^7}{4^3}\)

\(2^3\cdot2^5 = 2^8\\\\\dfrac{4^7}{4^3}= 4^{7-3}=4^4\\\\\mathrm{Since \;4 = 2^2, 4^4 = (2^2)^4=2^8}\)

\(4. \dfrac{\left(3x^{\frac{1}{3}}\cdot 3x^{\frac{7}{3}}\right)}{3x^{\frac{2}{3}}}\)

Answer:

55 in²

Step-by-step explanation:

Base x Height

The thermometer reading would be 73.48°C.

The boiling point of water is generally considered to be 100°C. According to the given information, the temperature of the liquid in the thermometer is 26.52°C lower than the boiling point of water. Therefore, to find the thermometer reading, we subtract 26.52 from 100.

100 - 26.52 = 73.48

Hence, the thermometer reading would be 73.48°C.

In this scenario, we are assuming that the thermometer is calibrated to measure temperature in Celsius. The boiling point of water at standard atmospheric pressure is 100°C, and the given information states that the liquid in the thermometer is 26.52°C lower than the boiling point.

By subtracting 26.52 from 100, we obtain a reading of 73.48°C.

Thermometers work by utilizing the principle that certain substances, such as mercury or alcohol, expand or contract with changes in temperature. The expansion or contraction is measured using a scale, which is marked with various temperature values.

In this case, the thermometer is calibrated in Celsius, so we refer to the Celsius scale. By subtracting 26.52 from 100, we find the temperature at which the liquid in the thermometer is settled, which is 73.48°C.

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Answer: -pi/4 and 3pi/4

Step-by-step explanation:

Whenever you're given an inverse trig function like this, think "tangent of what gives me -1?" There are multiple ways in which you can solve this; knowing how tangent work, guess checking sin/cos to get -1, or using a calculator. The only way tangent can be an integer is if the sine and cosine of the angle are equal.

The only spots on the pi circle where this happens is pi/4, 3pi/4, 5pi/4, and 7pi/4. Answers B and D are correct

Answer:

b

Step-by-step explanation:

just did it on edg 2020

Answer:

AB = 10.398

Step-by-step explanation:

By cosine rule, we have:

AB² = AC² + BC² - 2(AC)(BC)cos(ACB)

⇒ AB² = 7² + 10² - 2(7)(10)cos(73)

⇒ AB² = 49 + 100 - 140cos(73)

⇒ AB² = 149 - 140cos(73)

⇒ AB² = 149 - 140cos(73)

⇒ AB² = 149 - 140(0.292)

⇒ AB² = 149 - 40.88

⇒ AB² = 108.12

⇒ AB = √(108.12)

⇒ AB = 10.398

Answer:

53\(x_{123}\) == 134 cf

Step-by-step explanation:

A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a​

The height of the building is approximately 78.63 meters.

The following is a step-by-step explanation of how to solve the problem. We'll need to use some trigonometric concepts and formulas to find the solution.

Therefore, the height of the building is approximately 78.63 meters.

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Answer:

49 8/9 - 17 1/3 = -5/3 or -1 2/3