74,137 rounded to the nearest thousands is

Answer:

[tex]r[/tex]≈[tex]5.2 in[/tex]

Step-by-step explanation:

It is given that a circle is required to inscribe an equilateral triangle with an area of [tex]35.074 in^2[/tex] and an altitude of [tex]7.794 in[/tex],

Also, we know that the centroid divides the altitude into 2:1 form, thus

[tex]r=\frac{2}{3}(h)[/tex]

Substituting the value of an altitude, we have

[tex]r=\frac{2}{3}(7.794)[/tex]

[tex]r=5.196 in[/tex]

[tex]r[/tex]≈[tex]5.2 in[/tex]

Therefore, the radius of the circle is [tex]5.2 inches[/tex].

subtract the distance she traveled from the total distance she has to go

4 2/3 - 3 1/3 = 1 1/3 miles to go 

16,400 x (1 + 0.051)^20 =

16400 x (1.051)^20 =

16400 x 2.70429659 =

$44,350.46 

Answer:

As per the statement: Sandy is observing the velocity of a runner at different times.

Also, after one hour, the velocity of the runner is 4 km/h. and after two hours, the velocity of the runner is 2 km/h..

(A)

Let x represents the time in hours and y represents the velocity of the runner(in km/hr)

Then, we have two points from the given statement:

(1, 4) and (2, 2)

An equation of line for two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by;

[tex]y-y_1 = \frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

For the given two points (1, 4) and (2, 2) we have an equation:

[tex]y-4 = \frac{2-4}{2-1}(x-1)[/tex]

[tex]y-4 = \frac{-2}{1}(x-1)[/tex]

or

[tex]y-4 = -2(x-1)[/tex]

Using distributive property: [tex]a\cdot(b+c) = a\cdot b+ a\cdot c[/tex]

[tex]y-4 = -2x + 2[/tex]

Add 4 on both sides we get;

[tex]y-4 +4= -2x + 2+4[/tex]

Simplify:

[tex]y= -2x + 6[/tex]

Add 2x on both sides we get;

[tex]y + 2x=-2x+6+ 2x[/tex]

Simplify:

[tex]y + 2x = 6[/tex]

[Since, standard form for linear equations in two variables is Ax+By=C]

Therefore, an equation in two variables in the standard form that can be used to describe the velocity of the runner at different times is:

[tex]2x+y= 6[/tex] ; where x represents the time in hours and y represents the velocity of the runner.

(B)

Equation in part A

It is given as;  [tex]2x+y= 6[/tex]          .....[1]

To graph this equation; for the first 4 hours.

x                  y = -2x+6

1                  4

2                 2

3                 0

4                 -2

Now, using these points (1, 4) , (2, 2) , (3, 0) and (4, -2) plot the graph as shown below in the attachment.

Answer:  The required value of x is 16.

Step-by-step explanation:  Given that the value of y is 7 when the value of x is 8.

We are to find the value of x when y is 14.

The ratio of y to x is given by

[tex]y:x=7:8.[/tex]

Therefore, when y = 14, we must have

[tex]14:x=7:8\\\\\\\Rightarrow \dfrac{14}{x}=\dfrac{7}{8}\\\\\\\Rightarrow x=\dfrac{14\times8}{7}\\\\\Rightarrow x=16.[/tex]

Thus, the required value of x is 16.

Answer:

-9x+y=82

Step-by-step explanation:

hope this helped!

The equation y-10=9(x+8) can be transformed into standard form by distributing, simplifying, and rearranging terms to get 9x - y = -82.

The given equation is y-10=9(x+8), and we're asked to change this slope-intercept form into the standard form. First, we'll start by distributing the 9 to both x and 8 which will result in y-10 = 9x + 72. Then, we'll bring terms involving x and y to one side of the equation, leading to -9x + y = 82. This is almost in standard form, but typically we want the leading coefficient (the coefficient of x) to be positive, so we'll multiply the equation by -1. This gives us 9x - y = -82, which is the equation in standard form.

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The value of x is 12 and this can be determined by using the arithmetic operations and the given data.

Given :

40% is equal to the fraction x/30.

The following steps can be used in order to determine the value of 'x':

Step 1 - The arithmetic operations can be used in order to determine the value of 'x'.

Step 2 - According to the given data, the 40% is equal to the fraction x/30.

Step 3 - So, the value of X is calculated as:

[tex]\dfrac{40}{100}=\dfrac{x}{30}[/tex]

Step 4 - Simplify the above expression.

x = 12

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Using a calculator or long division, the square root of 658 is approximately 25.66.

To find the square root of 658, we can use a calculator or the long division method.

Using the long division method:

Step 1: Guess a number whose square is close to 658. Let's start with 25, since [tex]\(25^2 = 625\)[/tex], which is close to 658.

Step 2: Divide 658 by 25. [tex]\(658 \div 25 = 26.32\)[/tex]

Step 3: Take the average of the quotient and the divisor: [tex]\((25 + 26.32) \div 2 = 25.66\)[/tex]

Step 4: Repeat steps 2 and 3 using the new guess until the desired level of accuracy is achieved.

By repeating these steps, we'll get closer to the square root of 658. However, using a calculator will give a more accurate result.

Answer: Option (2) and (5) are the correct options.

Step-by-step explanation:

Since, the given expression, x+3.6= -1.7

If we add -3.6 in both sides then we get x+3.6+(-3.6)=1.7-3.6⇒x= -1.9

while,

If we subtract 3.6 from both sides then we get x+3.6-3.6=1.7-3.6⇒x= -1.9

Thus, In the above by adding -3.6 and by subtracting 3.6 we get the value of x in one step.(because after this only x remains in LHS of the given expression)

Therefore, Option (2) and (5) are correct.

Note: Except these two options we can not get x in one step. (we can not get single x in LHS of the given expression by the other options.)

Answer:

b e

Step-by-step explanation:

The domain of the function f(x) = x5 ln x consists of all positive real numbers since the natural logarithm is undefined for zero and negative numbers.

The domain of a function consists of all possible input values (x-values) where the function is defined. In the case of the function f(x) = x5 ln x, we need to consider where this function is defined.

The domain for a function that involves a natural logarithm (ln), like this one, is always x > 0. This is because the natural logarithm, or ln, is undefined for values of x <= 0. In other words, we can't take a natural logarithm of zero or a negative number.

Therefore, the domain of the function f(x) = x5 ln x is x > 0. All positive real numbers are included in the domain, while zero and negative numbers are excluded.

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Answer:

Step-by-step explanation:

Answer:

its  A

Step-by-step explanation:

Given: f(x) = 9 cos (2x)

The differential equation is df = - 18 sin(2x) dx

When x contrasts from π/6 to π/6 + 01, then dx = 0.1.
The variation in f is δf = - 18 sin(π/3) *(0.1) = -1.5588 ≈ -1.559

The computation in the change in f directly:

f(π/6) = 9 cos(π/3) = 4.5
f(π/6 + 0.1) = 9 cos(π/3 + 0.2) = 2.6818
δf = 2.6818- 4.5 = -1.6382 ≈ -1.638

Direct computation of δf is near to the real value but in error. 
The two outcomes will be closer as dx gets smaller.

Answer would be:
δf = -1.559  (correct answer)
δf = -1.638 (approximate answer)

Answer:

a

Step-by-step explanation:

His cost per wear

He will have 240 wears in 5 years

$180 in dry cleaning and $200 for cost of the suit.

$380 total investment

$1.58/per wear

The total investment for the suit is $380 and the cost per wear is $1.58.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

We have,

Jason decides to invest in a new two-piece suit which will cost him $200.

So, the total amount he invested

= $180 in dry cleaning + $200 for cost of the suit.

= $380

and, the cost per wear is

= 380/ 240

= $1.58

Learn more about Unitary Method here:

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