What is the equation of the line that passes through the points (3,6) and (-4,-8)

the answer is 16.0 or 11.0

Answer:

Step-by-step explanation:

The magnitude of an earthquake is a measure of the amount of energy released during the earthquake. A stronger magnitude generally means a more powerful earthquake.

The equation that could be used to represent this situation, where x is the course fee and R(x) is the total revenue, is: R(x) = 250000 + 375x - 2.5x²

Equations are mathematical statements with two algebraic expressionsοn either sideοf an equals (=) sign. It illustrates the equality between the expressions writtenοn the left and right sides. To determine the valueοf a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

N(x) = 625 + 2.5x

The revenue R(x) will be the productοf the numberοf students enrolled and the fee charged per student. The fee charged per student will be (400 - x) dollars. So, the revenue function can be represented as:

R(x) = (625 + 2.5x)(400 - x)

Simplifying the expression, we get:

R(x) = 250000 + 375x - 2.5x²

Therefore, the equation that could be used to represent this situation, where x is the course fee and R(x) is the total revenue, is:

R(x) = 250000 + 375x - 2.5x²

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Answer:

Yes

Step-by-step explanation:

functions include parabolas so yes!

Answer:

14

Step-by-step explanation:

You can solve it like this:

63x2=126

126/9=14

Answer:

530.087 trust me

Step-by-step explanation:

Supplier B would cost $600 more than supplier A. Then the correct option is B.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

A food production company is choosing between two suppliers of grain.

Let y be the cost and x be the number of bushels.

Supplier A sells grain for $5.25 per bushel plus a delivery fee of $3 per bushel.

y₁ = (5.25 + 3)x

y₁ = 8.25x

Supplier B sells the grain for $6.50 per bushel plus a flat delivery fee of $1,500 each week.

y₂ = 6.5x + 1500

Then the supplier would cost more if the production company bought 500 bushels of grain each week will be

For supplier A, we have

y₁ = 8.25 × 500

y₁ = $ 4125

For supplier B, we have

y₂ = 6.5 × 500 + 1500

y₂ = $ 4750

Then we have

y₂ - y₁ = 4750 - 4125

y₂ - y₁ = $ 625

Then the correct option is B.

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Answer:

-21

-29-(-8)=-21

Answer:

10 min.

Step-by-step explanation:

Answer:

6 minutes

Step-by-step explanation:

Based on the information given, the price of the zero coupon bond is $692.04.

To calculate the price of a zero coupon bond, we need to use the following formula:

\(\sf P =\dfrac{F}{1+r\div n}^{(nt)\)

Where:

Also, the annual interest rate is 7.50%, which is the market interest rate, and the compounding is semiannual, which means n = 2. Finally, the time to maturity is 5 years.

Plugging in the values into the formula, we get:

\(\sf P = \dfrac{1000}{(1+0.075\div2)^{(2\times5)}}\)

\(\sf P = \dfrac{1000}{(1.0375)^{10}}\)

\(\sf P = \dfrac{1000}{1.4450}\)

\(\sf P = \$692.04 \ \ (rounded \ to \ the \ nearest \ cent)\)

Therefore, the price of the zero coupon bond is $692.04.

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The distance between Basti and Cian is approximately 138.2 ft. Option D

To find the distance between Basti and Cian, we can use the Law of Sines, which relates the lengths of sides to the sines of their opposite angles in a triangle.

Let's label the points: A, B, and C. Ali is at point A, Basti is at point B, and Cian is at point C.

Given:

Angle ABC = 50 degrees (angle opposite side AC)

Angle BAC = 60 degrees (angle opposite side BC)

Ali is 150 ft away from Basti (side AB)

We want to find the distance between Basti and Cian, which is side BC.

Using the Law of Sines, we have:

BC/sin(50) = AB/sin(60)

Substituting the known values:

BC/sin(50) = 150/sin(60)

To find BC, we can rearrange the equation:

BC = (150/sin(60)) * sin(50)

Using a calculator to evaluate the expression:

BC ≈ 138.2 ft

Option D is correct.

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The crime that is often alcohol related is domestic violence. That is option D.

Domestic violence is defined as an abusive relationship that exist between two or more individuals that are closely related by blood or marriage.

The causes of domestic violence include the following:

Therefore, alcohol intake can lead to domestic violence because it can cause the abusive partner to have a reduction in cognitive and physical functions that impair self-control, with the consequent effect of reducing the ability to resolve conflicts nonviolently.

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Answer: 8  units

Step-by-step explanation:

The angle between the ground and the steepest slope on the real rollercoaster is approximately 89.998°.

A model rollercoaster is built to a scale of 1:32. In the model rollercoaster, the angle between the ground and the steepest slope is 110°.What is the angle between the ground and the steepest slope on the real rollercoaster?

To determine the angle between the ground and the steepest slope on the real rollercoaster, you need to consider the scale of the model rollercoaster.To find the real rollercoaster angle, you should use a scale factor that relates the model rollercoaster to the real one.

The scale factor should multiply the model angle to obtain the real one. Since the scale factor relates the model length to the real length, it should relate the horizontal distance and the vertical height.

The horizontal and vertical lengths are in a ratio of 32:1 for the model. This means that for every 32 units in the model, there is one unit in the real rollercoaster. Therefore, we can say that the horizontal length of the real rollercoaster is 32 times the horizontal length of the model rollercoaster.

That is:h(real) = 32h(model)Similarly, the vertical height of the real rollercoaster is 32 times the vertical height of the model rollercoaster. That is:v(real) = 32v(model)

The tangent of an angle equals the vertical height divided by the horizontal distance. Therefore, the tangent of the real angle equals the tangent of the model angle times the scale factor.

That is:tanθ(real) = 32tanθ(model)By substitution,θ(real) = arctan(32tanθ(model))For the given model angle of 110°,

the corresponding real angle is:θ(real) = arctan(32tan110°)θ(real) = arctan(32(-2.74747741945462))θ(real) = arctan(-87.91927694142864)θ(real) ≈ -89.998°

The negative sign indicates that the angle is measured below the horizontal line.

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Answer:

\(y=12\)

Step-by-step explanation:

The \(y\)-axis has equation \(x=0\), so the equation of a line perpendicular to the \(y\)-axis would be of the form \(y=c\).

The equation of this line given the point \((3,12)\) is \(y=12\).

Answer:

y = (1/2)x - 3

The slope is m = 1/2 and the y-intercept is (0, -3).

Step-by-step explanation:

Assuming that you meant 6y = 3x - 18, we solve this equation for y to obtain the slope-intercept formula y = mx + b for this particular case:

y = (3/6)x - (18/6), or

y = (1/2)x - 3

The slope is m = 1/2 and the y-intercept is (0, -3).

Answer:

  2) only one equation needs to be multiplied by something if y is to be eliminated.

  3) (x, y) = (-4, 0)

  4) (5, 2) satisfies the first equation, but not the second.

Step-by-step explanation:

You want to answer some questions about the use of elimination to solve the system ...

The coefficients of x are not multiples of each other, so both equations must be multiplied by something to eliminate the x-variable.

The coefficient of y in the first equation is -9 times the coefficient of y in the second equation. This means only the second equation needs to be multiplied by something (9) to eliminate the y-variable. Michael's observation is correct.

  (2x -9y) +9(5x +y) = (-8) +9(-20)

  47x = -188 . . . . . . . . . . simplify; the y-variable has been eliminated

  x = -4 . . . . . . . . . . . . divide by the coefficient of x

Y can be found by substitution:

  2(-4) -9y = -8

  -9y = 0 . . . . . . . . . add 8 to both sides

  y = 0 . . . . . . . . divide by -9

The solution is (x, y) = (-4, 0).

The solution is shown in part (3), and does not match (5, 2). No further proof is needed.

We suspect you're being asked to substitute the given point into at least one of the equations to show the equation is not satisfied. Trying the values in the second equation, we have ...

  5x +y = -20

  5(5) +(2) = 27 ≠ -20 . . . . (5, 2) is not the solution

__

Additional comment

The attached graph shows the offered point (5, 2) satisfies the first equation, so we choose to do the demonstration of part (4) using the second equation.

For standard form ax+by=c, the x- and y-intercepts are c/a and c/b, respectively. This means the intercepts for the first equation are a negative x-value and a positive y-value. The line will pass through the first quadrant.

For the second equation, both intercepts are negative, so the line has no presence in the first quadrant where the point (5, 2) is located.

The main difference between the random walk of a gas molecule and that of a protein molecule in water is that the gas molecule will have a lower random walk.

When there is a high frequency of molecules, as is the case in a liquid, there will be more random walks because molecules will keep bumping into each other. In gas however, the random walk will be less because molecules are more spaced out.

In conclusion, the gas molecule will have less random walk.

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Answer:

Step-by-step explanation:

A

Answer:7 x 2 − 14 x + 5

Step-by-step explanation:

1 In general, given a{x}^{2}+bx+cax  

2

+bx+c, the factored form is:

a(x-\frac{-b+\sqrt{{b}^{2}-4ac}}{2a})(x-\frac{-b-\sqrt{{b}^{2}-4ac}}{2a})

a(x−  

2a

−b+  

b  

2

−4ac

​

​

)(x−  

2a

−b−  

b  

2

−4ac

​

​

)

2 In this case, a=7a=7, b=-14b=−14 and c=5c=5.

7(x-\frac{14+\sqrt{{(-14)}^{2}-4\times 7\times 5}}{2\times 7})(x-\frac{14-\sqrt{{(-14)}^{2}-4\times 7\times 5}}{2\times 7})

7(x−  

2×7

14+  

(−14)  

2

−4×7×5

​

​

)(x−  

2×7

14−  

(−14)  

2

−4×7×5

​

​

)

3 Simplify.

7(x-\frac{14+2\sqrt{14}}{14})(x-\frac{14-2\sqrt{14}}{14})

7(x−  

14

14+2  

14

​

​

)(x−  

14

14−2  

14

​

​

)

4 Factor out the common term 22.

7(x-\frac{2(7+\sqrt{14})}{14})(x-\frac{14-2\sqrt{14}}{14})

7(x−  

14

2(7+  

14

​

)

​

)(x−  

14

14−2  

14

​

​

)

5 Simplify  \frac{2(7+\sqrt{14})}{14}  

14

2(7+  

14

​

)

​

  to  \frac{7+\sqrt{14}}{7}  

7

7+  

14

​

​

.

7(x-\frac{7+\sqrt{14}}{7})(x-\frac{14-2\sqrt{14}}{14})

7(x−  

7

7+  

14

​

​

)(x−  

14

14−2  

14

​

​

)

6 Simplify  \frac{7+\sqrt{14}}{7}  

7

7+  

14

​

​

  to  1+\frac{\sqrt{14}}{7}1+  

7

14

​

​

.

7(x-(1+\frac{\sqrt{14}}{7}))(x-\frac{14-2\sqrt{14}}{14})

7(x−(1+  

7

14

​

​

))(x−  

14

14−2  

14

​

​

)

7 Remove parentheses.

7(x-1-\frac{\sqrt{14}}{7})(x-\frac{14-2\sqrt{14}}{14})

7(x−1−  

7

14

​

​

)(x−  

14

14−2  

14

​

​

)

8 Factor out the common term 22.

7(x-1-\frac{\sqrt{14}}{7})(x-\frac{2(7-\sqrt{14})}{14})

7(x−1−  

7

14

​

​

)(x−  

14

2(7−  

14

​

)

​

)

9 Simplify  \frac{2(7-\sqrt{14})}{14}  

14

2(7−  

14

​

)

​

  to  \frac{7-\sqrt{14}}{7}  

7

7−  

14

​

​

.

7(x-1-\frac{\sqrt{14}}{7})(x-\frac{7-\sqrt{14}}{7})

7(x−1−  

7

14

​

​

)(x−  

7

7−  

14

​

​

)

10 Simplify  \frac{7-\sqrt{14}}{7}  

7 7−  14  to  1-\frac{\sqrt{14}}{7}1−  7 14

7(x-1-\frac{\sqrt{14}}{7})(x-(1-\frac{\sqrt{14}}{7}))

7(x−1−  7 /14 )(x−(1−  7 14 )) 11 Remove parentheses.

7(x-1-\frac{\sqrt{14}}{7})(x-1+\frac{\sqrt{14}}{7})

7(x−1−  7/ 14 .7(x−1+ 7 14 )

Answer:

See below for explanation

Step-by-step explanation:

The area of an isosceles triangle is \(A=\frac{1}{2}bh\), so let's write the base as an equation of y:

\(\displaystyle 9x^2+4y^2=36\\\\4y^2=36-9x^2\\\\y^2=9-\frac{9}{4}x^2\\\\y=\pm\sqrt{9-\frac{9}{4}x^2\)

As you can see, our ellipse consists of two parts, so the hypotenuse of each cross-section will be \(\displaystyle 2\sqrt{9-\frac{9}{4}x^2\), and each height will be \(\displaystyle \sqrt{9-\frac{9}{4}x^2}\).

Hence, the area function for our cross-sections are:

\(\displaystyle A(x)=\frac{1}{2}bh=\frac{1}{2}\cdot2\sqrt{9-\frac{9}{4}x^2}\cdot\sqrt{9-\frac{9}{4}x^2}=9-\frac{9}{4}x^2\)

Since we'll be integrating with respect to x because the cross-sections are perpendicular to the x-axis, then our bounds will be from -2 to 2 to find the volume:

\(\displaystyle V=\int^2_{-2}\biggr(9-\frac{9}{4}x^2\biggr)\,dx\\\\V=9x-\frac{3}{4}x^3\biggr|^2_{-2}\\\\V=\biggr(9(2)-\frac{3}{4}(2)^3\biggr)-\biggr(9(-2)-\frac{3}{4}(-2)^3\biggr)\\\\V=\biggr(18-\frac{3}{4}(8)\biggr)-\biggr(-18-\frac{3}{4}(-8)\biggr)\\\\V=(18-6)-(-18+6)\\\\V=12-(-12)\\\\V=12+12\\\\V=24\)

Therefore, this explanation confirms that the correct volume is 24!

Answer:

Shorter leg is 6

Step-by-step explanation:

In a 30°-60°-90° triangle, the hypotenuse is twice the length of the shorter leg. Therefore, if the hypotenuse is 12, then the shorter leg is 6.

Answer:

b = 4/3

Step-by-step explanation:

In an exponential equation:

f(x) = a (b)ˣ

Evaluated at x+1:

f(x+1) = a (b)ˣ⁺¹

The ratio between them is:

f(x+1) / f(x)

= (a (b)ˣ⁺¹) / (a (b)ˣ)

= b

So the decay factor b can be found by dividing the consecutive y values.

b = 16 / 12

b = 4/3

Answer:

y is just being multiplyed by -4 :)

Step-by-step explanation:

in other words -4x

Answer:

y = -4x

Step-by-step explanation:

Step-by-step explanation:

Find the product. Simplify your answer: (2b-3)(b - 2)

use the FOIL method. Multiply the: first, outer, inner, and last pairs:

\((2b-3)(b - 2)\\2b^2-4b-3b+6\\2b^2-7b+6\)

The solution to this equation: 42 +82=x² is x = 12.

A square number, also known as a perfect square, is an integer that is the square of another integer; in other words, it is the result of multiplying another integer by itself. For instance, 9 is a square number because it equals 32 and can be written as 3 3.

Instead of the product n n, the equivalent exponentiation n2, which is typically pronounced "n squared," is used to represent a number's square. The name of the shape is where the term "square number" originated. The area of a unit square (1 × 1) is the unit of area.

The solution to this equation: 42 +82=x²

x = √(42 +82)

x = √(144)

x = 12

Thus, The solution to this equation: 42 +82=x² is x = 12.

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Answer:

The answer would be D.9