A recipe uses 6 cups of cheese to serve 30 people. How much cheese is needed for 50 people

Answer:

-9x+y=82

Step-by-step explanation:

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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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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.

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:

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: 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:

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].

Final answer:

The unit rate, or average speed, for traveling 4543.08 km in 52.4 hours is calculated by dividing the distance by the time, resulting in an average speed of 86.70 km/h.

Explanation:

The question asks for the unit rate of 4543.08 km traveled in 52.4 hours, which is essentially asking for the average speed in kilometers per hour (km/h). To find this, you would divide the total distance traveled by the total time taken.

Mathematically, this is expressed as:

Substituting the given values:

Therefore, the unit rate or average speed is 86.70 km/h. It's important to note that when calculating such problems, it's essential to maintain consistency in the units (in this case, km for distance and hours for time) to ensure the accuracy of your result.

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 

Answer:

its  A

Step-by-step explanation:

Answer:

Option D is correct

Solution = (-1, -2)

Step-by-step explanation:

Given the equation:

y = x – 1               ....[1]

y = 3x + 1            ....[2]

Equate equation [1] and [2] to solve for x.

[tex]x-1=3x+1[/tex]

Subtract x from both sides we have;

[tex]-1=2x+1[/tex]

Subtract 1 from both sides we have;

[tex]-2=2x[/tex]

Divide both sides by 2 we have;

x = -1

Substitute the value of x = -1 in [1] we have;

y=-1-1 = -2

Graphically:

Graph the system of equations as shown below.

The intersection point of these lines is the solution for the given system of equation

⇒ (-1, -2)

Therefore, the solution for the given system of equation is, (-1, -2)

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.

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

For more information, refer to the link given below:

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Answer:

Step-by-step explanation: