the price of a stove is s dollars. Pedro makes 10% down payment for a two year installment purchase. The monthly payment is m dollars. Express the finance charge algebraically.

Answer:

0.38

Step-by-step explanation:

Percentage is number/100 = 38/100 = 0.38

Cheers

Dividend ÷ Divisor = Quotient and Remainder

When a dividend is divided by a divisor, we get the value of the quotient in the result.

The result of dividing one integer by another is the quotient. For example, in 8 ÷4 = 2, the division result is 2, hence the quotient is 2. The dividend is eight, while the divisor is four.

The derivative of a quotient is the denominator times the numerator's derivative minus the numerator times the denominator's derivative, all divided by the denominator's square, according to the Quotient Rule.

When dividing one exponential equation by another, we use this rule. We must subtract the exponent in the denominator from the exponent in the numerator using the quotient formula, but the bases must be the same.

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The distance between the lines L1 and L2 given by √293/7.

The distance is the angular separation between any two points on one line. Eventually, the smallest distance between these lines is zero. The distance between the lines is the same length as the perpendicular between them.

Finding two locations P1 and P2 on L1 and L2 separately will help us determine the shortest path between them. We then need to project P1P2 in the direction n that is perpendicular to both L1 and L2 to arrive at the answer. To put it another way, L1 - L2 distance = COMPN (P1P2).

Let the two points be

[tex]$$\begin{aligned}& \vec{r}=\hat{1}+2 \hat{j}-4 \hat{k}+\lambda(2 \hat{i}+3 \hat{j}+6 \hat{k}) \\& \vec{r}=3 \hat{i}+3 \hat{j}-5 \hat{k}+\mu(2 \hat{i}+3 \hat{j}+6 \hat{k})\end{aligned}$$[/tex]

These two lines pass through the points having position vectors [tex]$\overrightarrow{a_1}=\hat{i}+2 \hat{j}-4 \hat{k}$[/tex]and [tex]$\overrightarrow{a_2}=3 \hat{i}+3 \hat{j}-5 \hat{k}$[/tex] are parallel to the vector [tex]$\vec{b}=2 \hat{i}+3 \hat{j}+6 \hat{k}$[/tex]

Now, [tex]$\overrightarrow{a_2}-\overrightarrow{a_1}=3 \hat{i}+3 \hat{j}-5 \hat{k}-\hat{i}-2 \hat{j}+4 \hat{k}=2 \hat{i}+\hat{j}-\hat{k}$[/tex] and [tex]$\left(\overrightarrow{a_2}-\overrightarrow{a_1}\right) \times \vec{b}=(2 \hat{i}+\hat{j}-\hat{k}) \times(2 \hat{i}+3 \hat{j}+6 \hat{k})$[/tex]

[tex]$$\begin{aligned}& =\left|\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \\2 & 1 & -1 \\2 & 3 & 6\end{array}\right| \\& =\hat{i}(6+3)-\hat{j}(12+2)+\hat{k}(6-2) \\& =9 \hat{i}-14 \hat{j}+4 \hat{k}\end{aligned}$$[/tex]

[tex]$$\left|\left(\overrightarrow{a_2}-\overrightarrow{a_1}\right) \times \vec{b}\right|=\sqrt{9^2+(-14)^2+4^2}=\sqrt{81+196+16}=\sqrt{293}$$\pi[/tex]

and [tex]$|\vec{b}|=\sqrt{2^2+3^2+6^2}=\sqrt{4+9+36}=7$[/tex]

The shortest distance between the two lines exists given by [tex]$\frac{\left|\left(\overrightarrow{\mathrm{a}_2}-\overrightarrow{\mathrm{a}_1}\right) \times \overrightarrow{\mathrm{b}}\right|}{|\overrightarrow{\mathrm{b}}|}=\frac{\sqrt{293}}{7}$[/tex]

Therefore, the distance between the lines L1 and L2 given by √293/7.

The complete question is;

Find the distance between the lines L1 and L2 given by

[tex]$$\vec{r}=\hat{1}+2 \hat{j}-4 \hat{k}+\lambda(2 \hat{i}+3 \hat{j}+6 \hat{k}) \text { and } \vec{r}=3 \hat{i}+3 \hat{j}-5 \hat{k}+\mu(2 \hat{i}+3 \hat{j}+6 \hat{k})$$[/tex]

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Step-by-step explanation:

1 gallon = 3.785411784... liters

so, you can pour 3 whole liters into the container.

it you pour 4 liters, the container will overflow.

1 gallon is more than 3 liters, but less than 4 liters.

The solution to the system of equations is x = −2, y = ±√23.

Equation is a math statement that expresses two expressions with an equal sign. It is used to find the value of an unknown variable or unknowns. Equations are used in many branches of mathematics and science. For example, equations are used to calculate the force of gravity, the speed of light, the temperature of a gas, and the area of a triangle. Equations are also used to solve problems in physics, chemistry, engineering, and other disciplines. Equations are written in symbols and often involve multiple equations.

This system can be solved by solving the two equations separately.

For the first equation, xe^y+2e^y= 0, we can rearrange it to get xe^y = −2e^y. We can then divide both sides by e^y to get x = −2.

For the second equation, x² − 3x + y² = 19, we can plug in the value of x that we found previously, x = −2, and rearrange the equation to get y² = 23, and then solve for y by taking the square root of both sides, giving y = ±√23.

Therefore, the solution to the system of equations is x = −2, y = ±√23.

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Answer:

yes

Step-by-step explanation:

replace both x and y in the equation with 3 and solve, you will get 3=3 so its true

Answer:

No

Step-by-step explanation:                                 x  y

First thing you have to do is plug y in for y. (3,3)

y= -2x+3

3= 2x+3

Then plug in x for x.

3 = -2(3) +3

Then solve the problem.

3= -6+3

3 = -3

From there we can tell that negative 3 is not the same as positive 3. Another thing you can do is go to desmos graphing calculator and type the equation in and see where the point (3,3) is located and notice that it does not go through the line from the equation.

The line segment which is divided into the ratio 2 : 3 represents that line is divided into 5 equal parts.

As given in the question,

Let the given line segment be represents as AB .

And point C be the points which divide AB in the ratio 2 : 3.

The given ratio represents from AC is divided into 2 equal parts.

And BC is divided into 3 equal parts.

Total number of parts AB is divided into the ratio 2 : 3 is equal to

= 2 + 3

= 5 equal parts

Therefore, the line segment divided into the ratio 2 : 3 represents 5 equal parts.

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Answer:

$280

Step-by-step explanation:

30% of 400=120, 400-120=280

Answer:

u draw a square

Step-by-step explanation:

Option 1 is Correct. For the line connecting the two locations, an equation in slope-intercept form is. y = x + 3

A line's slope and intercept give information on its steepness and the point at which it crosses an axis, respectively. The linear relationship between two variables is defined by the slope and intercept, which can be used to calculate the average rate of change.

When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilize the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula.

y=mx+c

y= (6+3)/(4+2)

y= 9/6

y= 3/2

equation = y+6 =3/2(x-2)

2y+12=3x-6

y=x-3

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Correct Question:

Write an equation in slope-intercept form for the line passing through the pair of points. (2, –6), (–4, 3) Question 1 options:

1. y = x + 3

2. y = x – 3

3. y = x – 3

4. y = x + 3

Answer: d 135 ft

Step-by-step explanation:

For r [tex]$\mathrm{k}=0$[/tex]or[tex]$\mathrm{k}=3$,[/tex] the given equation will be a perfect square.

[tex]$$(4-k) x^2+(2 k+4) x+8 k+1=0$$[/tex]

Here, [tex]$a=4+k, \quad b=2 k+4, \quad c=8 k+1$[/tex]

The given equation will be a perfect square, i.e., real and equal roots if

[tex]& \mathrm{D}=0 \\[/tex]

[tex]& \mathrm{~b}^2-4 \mathrm{ac}=0 \\[/tex]

[tex]& (2 \mathrm{k}+4)^2-4(4-\mathrm{k})(8 \mathrm{k}+1)=0 \\[/tex]

Then,

[tex]& 4 \mathrm{k}^2+16+16 \mathrm{k}-4\left(32 \mathrm{k}-8 \mathrm{k}^2+4-\mathrm{k}\right)=0 \\[/tex]

Simplifying,

[tex]& \mathrm{k}^2+4+4 \mathrm{k}-32 \mathrm{k}+8 \mathrm{k}^2-4+\mathrm{k}=0 \\[/tex]

[tex]& 9 \mathrm{k}^2-27 \mathrm{k}=0 \\[/tex]

[tex]& \mathrm{k}^2-3 \mathrm{k}=0 \\[/tex]

So,

[tex]& \mathrm{k}(\mathrm{k}-3)=0 \\[/tex]

Get,

[tex]& \mathrm{k}=0[/tex] or [tex]\mathrm{k}=3[/tex]

Hence for [tex]$\mathrm{k}=0$[/tex]or[tex]$\mathrm{k}=3$,[/tex] the given equation will be a perfect square.

The complete question is,

For what value of [tex]$\mathrm{k},(4-\mathrm{k}) \mathrm{x}^2+(2 \mathrm{k}+4) \mathrm{x}+(8 \mathrm{k}+1)=0$[/tex] is a perfect square:

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For  k=0 or k=3, the given equation will be a perfect square.

4−k)x 2 +(2k+4)x+8k+1=0

Here, a=4+k,b=2k+4,c=8k+1

The given equation will be a perfect square, i.e., real and equal roots if

D=0

b2 −4ac=0

(2k+4) 2 −4(4−k)(8k+1)=0

4k 2 +16+16k−4(32k−8k 2+4−k)=0

k 2+4+4k−32k+8k 2−4+k=0

9k 2−27k=0

k 2−3k=0

k(k−3)=0

k=0 or k=3

Hence for k=0 or k=3, the given equation will be a perfect square.

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This is a linear system since it is a linear combination of the inputs x[n] and x[n-1].

A: y[n] = x[n] x x[n-1]

This is a linear system since it is a linear combination of the inputs x[n] and x[n-1]. We can represent this equation as:

y[n] = a * x[n] + b * x[n-1]

where a and b are constants.

For example, if x[n] = 2 and x[n-1] = 3 then y[n] = 2 x 3 = 6.

C: y[n] = x2[n]

This is also a linear system since it is a linear combination of the input x[n] and its squared value x2[n]. We can represent this equation as:

y[n] = c * x[n] + d * x2[n]

where c and d are constants.

For example, if x[n] = 2 then y[n] = c * 2 + d * 2² = c * 2 + d * 4.

Therefore, the correct answer is D: (a) and (c).

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The work done in lifting a forty-pound crate three feet is forty-three foot-pounds

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Answer: $16

Hope this helps :)

Step-by-step explanation:

Find the unit rate and multiply by 50

1 Dozen=12 Eggs

1 Dozen= $3.84

3.84/12= .32 per egg

.32*50= 16

The answer of 5 less than 10 is 5.

The answer of 5 less than 10 is 5 which can be derived using simple mathematical calculations.

To find 5 less than 10, you can subtract 5 from the original number 10.

10 - 5 = 5

It's a simple arithmetic operation where you subtract a specific number, in this case, 5, from the original number.

An arithmetic operation is a mathematical process that combines two or more numbers to produce a new number. The most basic arithmetic operations are addition, subtraction, multiplication, and division.

Addition: It is the process of combining two or more numbers to find their sum. For example, 2 + 3 = 5 is an addition operation.

Subtraction: It is the process of finding the difference between two numbers. For example, 5 - 3 = 2 is a subtraction operation.

Multiplication: It is the process of finding the product of two or more numbers. For example, 3 x 4 = 12 is a multiplication operation.

Division: It is the process of finding the quotient of two numbers. For example, 12 ÷ 3 = 4 is a division operation.

Therefore, The answer of 5 less than 10 is 5.

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Answer:

y = 154°

Step-by-step explanation:

Because angle z is a straight angle it is 180°.

26° + y = 180°

subtract 26.

y = 154°

The correlation coefficient, r, is a unitless measure and it is not affected by the units of measurement of the variables. Changing the units of measurement of one or both variables will not change the correlation coefficient.

If heart disease death rate were expressed as deaths per 1,000 people instead of as deaths per 100,000 people, the correlation r between wine consumption and heart disease death rate would not change. The strength and direction of the linear link between two variables is measured by the correlation coefficient, or r.

The correlation coefficient is calculated by taking the covariance of the two variables and dividing it by the product of the standard deviations of the two variables. The covariance is a measure of how two variables vary together, and it is not affected by the units of measurement.

The standard deviation is also not affected by the units of measurement, as it is a measure of how much the data deviates from the mean.

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The growth rate of [tex]r=100\left[\left(\frac{H(r)}{6240}\right)^{1 / t}-1\right][/tex] the number of households is increasing.

Compound growth is the average rate of growth that an investment experience over a number of years. When contemplating the investing landscape, one way to think about the compound growth rate is that it accounts for all the hills and valleys.

The % increase is simply divided by N, the number of years, to get the yearly percentage growth rate.

The number of households initially =P=6240

We have the value of Time period = t=3 years

As after three years the total number of households becomes =A=7800

Now

[tex]$$\begin{aligned}7800 & =6240\left(1+\frac{r}{100}\right)^8 \\\frac{7800}{6240} & =\left(1+\frac{r}{100}\right)^3 \\\left(1+\frac{r}{100}\right) & =\sqrt[3]{\frac{7800}{6240}}=1.0772 \\\frac{r}{100} & =1.0772-1=0.0772 \\\end{aligned}$$[/tex]

r =7.72% per year

Further solving we can write it as:

[tex]$$\begin{aligned}& H(r)=6240\left(1+\frac{r}{100}\right)^t \\& \left(\frac{H(r)}{6240}\right)^{1 / t}=\left(1+\frac{r}{100}\right) \\& \left(\frac{H(r)}{6240}\right)^{1 / t}-1=\frac{r}{100} \\& r=100\left[\left(\frac{H(r)}{6240}\right)^{1 / t}-1\right]\end{aligned}$$[/tex]

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Answer:

  (c)  x = 6 and y = 1

Step-by-step explanation:

You want to know the values of x and y that make the set {2xy, x²-y², x²+y²} equal to the set {12, 35, 37}.

There are two clues that help you here:

The values of x and y are (x, y) = (6, 1).

your answer is in given picture just go through them

If the ordered pair is located on the graph of the linear equation, then it is a solution to the equation.

If you are looking at the graph of a linear equation, you can determine whether an ordered pair is a solution by seeing if the point representing the ordered pair is on the line of the equation. If the point is on the line, then the ordered pair is a solution to the equation. If the point is not on the line, then it is not a solution to the equation. The line of the equation will pass through all of the points that are solutions to the equation and all other points will not be on the line. This means that if you have an ordered pair and you want to know if it is a solution, you can look at the graph and see if it is on the line. If it is on the line, then it is a solution.

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After calculating the average of his last 4 years’ salaries and will give him 1. 9% of that average for each year he worked, the total pension is $2928.204.

In the given question, we have to calculate Henry pension.

Henry has worked for a factor for 31 years and will be retiring.

He earned salaries over the past 4 years of $38433, $37776, $39125, and $38782.

His employer calculates pension by finding the average of his last 4 years’ salaries and will give him 1.9% of that average for each year he worked.

His earning over the past 4 years = $38433, $37776, $39125, $38782

The average of Henry earning = Sum of his earning over 4 years / number of years

The average of Henry earning = ($38433 + $37776 + $39125 + $38782)/4

The average of Henry earning = $154,116/4

The average of Henry earning = $38,529

Hence, the average of Henry last 4 years’ salaries is $38,529.

The pension is 1.9% of the average salary. So,

Pension = $38,529×1.9%

Pension = $38,529×0.019

Pension = $732.051

He worked for total 4 years. So,

Total pension = $732.051×4

Total pension = $2928.204

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The given expression is of the form y=mx+c. Comparing, we get the slope as 7.

The direction and steepness of a line are represented numerically by the slope or gradient of the line. It provides the ratio of how much y rises when x rises by a particular amount. The general form is therefore y=mx+c, where c represents the y-intercept and m represents the slope. This form gives the slope-intercept form.

Given the expression is  y=7x+3. Comparing this expression with the general form we get, slope or gradient as 7 and y-intercept as 3. Therefore, the required answer is 7.  

The complete question -

What is the gradient of the line y=7x+3?

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The required expression gives the rate of change will be d'(5) at which the depth is changing at 5 minutes.

Let d(t) represent the depth of the rain puddle at any time t,

⇒ d(t)  ....(i)

The depth is changing with respect to time, which is given in the question

Differentiate equation (i) with respect to t and we get

⇒δd(t)/δt = d'(t) ....(ii)

This is the rate of change in depth unit time:

As per the question, the depth is changing at 5 minutes

Substitute the value of t=5 in equation (ii), and we get

⇒ d'(5)

Therefore, the required expression gives the rate of change will be d'(5).

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Answer:

[tex]3x^2+4x+8[/tex]

Step-by-step explanation:

To find the value of [tex]7x^2+6x+9-4x^2-2x-1[/tex]

We need to combine like terms by grouping

[tex]7x^2-4x^2+6x-2x+9-1[/tex]

= [tex]3x^2+4x+8[/tex]

Hope this helps :)

Have a great day!

Answer:

[tex]y=\frac{1}{6}x + 1[/tex]

Step-by-step explanation:

12y - 2x= 12

12y= 2x + 12

/12          /12

y = 1/6x +1