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Answer:

The correct option is C.

Step-by-step explanation:

The given equation is

[tex]3x-\frac{1}{5}-\frac{2}{9}x=\frac{124}{5}[/tex]

If two terms have the same variables having same powers, then they are known as like terms.

In the given equation [tex]3x[/tex] and [tex]-\frac{2}{9}x[/tex] are like terms.

So, when we simplify the given equation by combining like terms. we need to combined [tex]3x[/tex] and [tex]-\frac{2}{9}x[/tex] .

Therefore the correct option is C.

The solution to the equation is approximately x = 45.48.

To solve the equation 3x - 1/5 - 2/9x = 124/5,  to combine like terms. Like terms are terms that have the same variable and exponent.

The terms in the equation are:

3x (coefficient is 3, and the variable is x)

-1/5 (coefficient is -1/5)

-2/9x (coefficient is -2/9, and the variable is x)

Now, let's identify the like terms that  combined:

C) 3x and -2/9x

The terms 3x and -2/9x both have the variable x, so they are like terms and can be combined.

Step 1: Combine the like terms:

3x - 2/9x = (3 - 2/9)x = (27/9 - 2/9)x = (25/9)x

Now, after combining the like terms, the equation becomes:

(25/9)x - 1/5 = 124/5

Step 2: Isolate x on one side of the equation. To do this, we can first get rid of the fraction by multiplying the entire equation by the least common multiple (LCM) of the denominators, which is 45 (LCM of 9 and 5):

45 × [(25/9)x - 1/5] = 45 × (124/5)

This simplifies to:

25x - 9 = 1128

Step 3: Now, isolate x by moving the constant term (-9) to the other side of the equation:

25x = 1128 + 9

25x = 1137

Step 4: Finally, divide by 25 to solve for x:

x = 1137 / 25

x ≈ 45.48

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We are given point (2,5).

We need to find the equation of line perpendicular to the given line and passes through the point (2, 5).

We know point-slope form :

y-y1 = m(x-x1).

Plugging values of (x1,y1) = (2,5) in above slope-intercept form, we get

y - 5 = m(x-2).

Which matches 3rd option y − 5 = −(x − 2).

Answer:

The answer is C.

Step-by-step explanation:

25 candles

What is profit and loss ?

Profit or Gain = Selling price – Cost Price

Loss = Cost Price – Selling Price

According to the given question,

Candles sold must cover the expenses = 100

Let x be the no. of candles that needs to be sold to cover the expenses

rent = 100

Cost price of 1 candle = CP = 1

Cost price of x candles = CP = 1x

Selling price of 1 candle = SP = 5

Selling price of x candles = SP = 5x

Therefore, from the above statements we can infer that the profit generated must be equal to the expenses,

So, SP - CP = Profit = 100

5x - x  = 100

4x = 100

x = 25

Therefore, we need 25 candles that needs to be sold to cover the expenses

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Final answer:

The correct function is B, 3log_5(x-4), which represents a logarithmic function that is vertically stretched by a factor of 3 and translated 4 units to the right.

Explanation:

The student is asking about transformations of a parent function, specifically a vertical stretch and a horizontal translation. When a function is vertically stretched by a factor of 3, this involves multiplying the function by 3. A translation of 4 units to the right would mean adjusting the input variable x by subtracting 4. Considering the options given, option B, 3log5(x-4), is the correct answer because it represents a function that has been vertically stretched by a factor of 3 and horizontally translated 4 units to the right from its parent function log5x.

Answer:

it take 31.53 minutes to run the entire race

it take 6.3 minutes to run the 1 km

Step-by-step explanation:

A runner ran 2/3 of a 5 kilometer race in 21 minutes. They ran the entire race at a constant speed.

[tex]\frac{2}{3} \cdot 5= \frac{10}{3}[/tex]

3.33 km is covered in 21 minutes

So 5 km is covered in [tex]\frac{5 \cdot 21}{3.33}=31.53[/tex]minutes

it take 31.53 minutes to run the entire race

[tex] \frac{10}{3}[/tex] km is covered in 21 minutes

1 km is covered in [tex]\frac{21}{\frac{10}{3} } =6.3[/tex]

It takes to run the entire race is 31 minutes and 30 seconds and it takes to run 1 kilometer is 6 minutes and 18 seconds.

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

[tex]\rm speed = \dfrac{distance}{time}[/tex]

A runner ran 2/3 of a 5 kilometers race in 21 minutes. They ran the entire race at a constant speed.

2/3 of 5 km is given as x

[tex]x = \dfrac{2}{3}* 5 = \dfrac{10}{3}[/tex]

Then the speed will be

[tex]\rm speed = \dfrac{\frac{10}{3}}{21} = \dfrac{10}{3*21} = \dfrac{10}{63}[/tex]

a. It takes to run the entire race will be

[tex]\rm Time = \dfrac{5}{ \frac{10}{63}} = \dfrac{63* 5 }{10} =31.5[/tex]

It takes to run the entire race is 31 minutes and 30 seconds.

B.  It takes to run 1 kilometer will be

[tex]\rm Time = \dfrac{1}{ \frac{10}{63}} = \dfrac{63* 1}{10} = 6.3[/tex]

It takes to run 1 kilometer is 6 minutes and 18 seconds.

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Answer:

[tex]x_{1}=4\\x_{2}=2\\ x_{3}=3[/tex]

Step-by-step explanation:

The given expression is

[tex]f(x)=x^{3}-9x^{2} +26x-24[/tex]

First, we need the divisors of the independent term, which is 24.

24 divisors: 1, 2, 3, 4, 6, 8, 12, 24.

Now, we replace each divisor in the function, and those which gives zero as result, those are gonna be the roots of the equation.

For [tex]x=1[/tex]

[tex]f(1)=(1)^{3}-9(1)^{2} +26(1)-24=1-9+26-24=-6[/tex]

This means [tex]x=1[/tex] is not a solution.

For [tex]x=2[/tex]

[tex]f(2)=(2)^{3}-9(2)^{2} +26(2)-24=8-36+52-24=0[/tex]

So, [tex]x=2[/tex] is the first solution.

For [tex]x=3[/tex]

[tex]f(3)=(3)^{3}-9(3)^{2} +26(3)-24=27-81+78-24=0[/tex]

It's solution.

For [tex]x=4[/tex]

[tex]f(4)=(4)^{3}-9(4)^{2} +26(4)-24=64-144+104-24=0[/tex]

Therefore, all roots are

[tex]x_{1}=4\\x_{2}=2\\ x_{3}=3[/tex]

Answer:

C. p → q

Step-by-step explanation:

We are given that,

'p' is represented by 'x = 4' and 'q' is represented by 'y = -2'.

That is, we have,

p: x = 4

q: y = -2

The given statement is, 'If x = 4, then y = -2'.

This means that whenever x = 4, then y = -2.

That is, 'x = 4 implies y = -2'.

Thus, it will be represented by p → q.

To get the probability of two individual events both occurring, you have to multiply the probabilities of their individual events occurring. Therefore in this problem, the probability that a student selected at random will pass both French 101 and French 102 is 0.683 (.75 x .91). The answer is already rounded to three decimal places.

The height of the fountain is 43.20m

Data;

The circumference of a circle is given as

[tex]c = 2\pi r[/tex]

Let's calculate the radius of the circle

[tex]c=2\pi r\\r=c/2\pi \\r=190/(2*3.14)\\r=30.25m[/tex]

Assuming the radius of the pool makes a right angle triangle with the top of the fountain;

[tex]tan\theta=\frac{opposite}{adjacent}\\tan55=\frac{x}{30.25}\\ x= 30.25tan55\\x=43.20m[/tex]

From the calculations above, the height of the fountain is 43.20m

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