Mathematics College

Solve: 3x-15 over 2=4x

A. 11

B. 6

C. -3

D. -15

Answers

Answer 1
C.-3
x=-3

3x-15/2=4x
multiply 2 on both sides
3x-15=8x
subtract 3x from both sides
-15=5x
divide 5 from both sides
-3=x
Answer 2
Your answer is C) -3.

Here is my work:

3x-15/2=4x
=3x-15=8x
=-15=5x
=-3=x

Related Questions

equivalent ratios number 1 to 50

Answers

are you meaning something like 1 to 50= 2 to 100 or something like 1 to 50, 1:50,1/50 they all r the same??
2:100 will be equivalent to 1:50

How do you solve an inequality

Answers

We can often solve inequalities by adding or subtracting a number from both sides

Answer:

you solve an inequality by doing the inverse equation on each side of the equation.

Step-by-step explanation:

Write twelve and sixteen thousand as a mixed decimal

Answers

12.016

hope this helps

√10, π, 3.5
order least to greatest

Answers

π, √10, 3.5

3.14, 3.16, 3.5
From least to greatest, we have:
___________________________________
" π , √10 , 3.5 " .
___________________________________

We have:  "3.5" (given) ;

                 " π " = 3.14159...

                "√10" = 3.162277660168379
___________________________________
So, from least to gretest, we have:
___________________________________
 " π , √10 , 3.5 " .
___________________________________

What are 5 numbers that have 3,5, and 7 as prime factors

Answers

105,210,315,420,525 Hope I helped! ^_^

he bought 8 pizzas to be shared equally among 40 people. what is the equivalent representation

Answers

8/40 or 0.2 is your answer.

Find the gradient of the function at the given point. function point f(x, y, z) = x2 + y2 + z2 (3, 9, 8)

Answers

Answer:

[tex]\displaystyle \nabla f(3, 9, 8) = 6 \hat{\i} + 18 \hat{\j} + 16 \hat{\text{k}}[/tex]

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

Derivative Rule [Basic Power Rule]:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Multivariable Calculus

Differentiation

Partial DerivativesDerivative Notation

Gradient:                                                                                                             [tex]\displaystyle \nabla f(x, y, z) = \frac{\partial f}{\partial x} \hat{\i} + \frac{\partial f}{\partial y} \hat{\j} + \frac{\partial f}{\partial z} \hat{\text{k}}[/tex]

Gradient Property [Addition/Subtraction]:                                                          [tex]\displaystyle \nabla \big[ f(x) + g(x) \big] = \nabla f(x) + \nabla g(x)[/tex]

Gradient Property [Multiplied Constant]:                                                            [tex]\displaystyle \nabla \big[ \alpha f(x) \big] = \alpha \nabla f(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify.

[tex]\displaystyle f(x, y, z) = x^2 + y^2 + z^2[/tex]

[tex]\displaystyle P(3, 9, 8)[/tex]

Step 2: Find Gradient

[Function] Differentiate [Gradient]:                                                             [tex]\displaystyle \nabla f = \frac{\partial}{\partial x} \Big( x^2 + y^2 + z^2 \Big) \hat{\i} + \frac{\partial}{\partial y} \Big( x^2 + y^2 + z^2 \Big) \hat{\j} + \frac{\partial}{\partial z} \Big( x^2 + y^2 + z^2 \Big) \hat{\text{k}}[/tex][Gradient] Rewrite [Gradient Property - Addition/Subtraction]:                [tex]\displaystyle \nabla f = \bigg[ \frac{\partial}{\partial x}(x^2) + \frac{\partial}{\partial x}(y^2) + \frac{\partial}{\partial x}(z^2) \bigg] \hat{\i} + \bigg[ \frac{\partial}{\partial y}(x^2) + \frac{\partial}{\partial y}(y^2) + \frac{\partial}{\partial y}(z^2) \bigg] \hat{\j} + \bigg[ \frac{\partial}{\partial z}(x^2) + \frac{\partial}{\partial z}(y^2) + \frac{\partial}{\partial z}(z^2) \bigg] \hat{\text{k}}[/tex][Gradient] Differentiate [Derivative Rule - Basic Power Rule]:                  [tex]\displaystyle \nabla f = 2x \hat{\i} + 2y \hat{\j} + 2z \hat{\text{k}}[/tex][Gradient] Substitute in point:                                                                     [tex]\displaystyle \nabla f(3, 9, 8) = 2(3) \hat{\i} + 2(9) \hat{\j} + 2(8) \hat{\text{k}}[/tex][Gradient] Evaluate:                                                                                     [tex]\displaystyle \nabla f(3, 9, 8) = 6 \hat{\i} + 18 \hat{\j} + 16 \hat{\text{k}}[/tex]

∴ the gradient of the function at the given point is <6, 18, 16>.

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Topic: Multivariable Calculus

Unit: Directional Derivatives

Help with Precalc Vectors? Medal and fan v = (-7,8) Find the magnitude of vector v. Express your answer in radical form sqrt of 113 is what I got for that. second part: use the magnitude and the angle of vector v to write it in the form (lvlcostheta, lvl sin theta). I don't know how to determine the single angle for one vector. Earlier in a different part of the problem, I was asked to find the angle between two vectors, but I don't think you use that here since no second vector is provided. So how would I answer the second part? Thanks(:

Answers

Hello Kaviipik!
Lets find the mag of v = (-7,8). Since we have one order pair we are finding the mag from the origin.
Yes we are using Pythagorean Theorem to calculate the magnitude
[tex]a^2 + b^2 = c^2[/tex] 

[tex]\sqrt{v^2} = \sqrt{(-7)^2 + (8)^2}[/tex]
[tex]v = \sqrt{(-7)^2 + (8)^2}[/tex]
[tex]v = \sqrt{49 + 64}[/tex]
[tex]v = \sqrt{113}[/tex]
[tex]v = \sqrt{113} = 10.6301458[/tex]
Now  we use 
[tex]\theta = tan^{-1} (\frac{b}{a})[/tex]
[tex]\theta = tan^{-1} (\frac{8}{-7})= 48.8[/tex]
[tex](\sqrt{113} \times cos(48.8) , \sqrt{113} \times sin(48.8) )[/tex]

Final answer:

To express the vector v = (-7,8) in the form (|v|cosθ, |v|sinθ), you first correctly found the magnitude |v| using the Pythagorean theorem. Then, to find the angle θ, use the arctangent function applied to the y/x components of your vector. Ensure the angle is in the correct quadrant by modifying it if necessary.

Explanation:

To find the magnitude of the vector v = (-7,8), you've correctly done the Pythagorean theorem and found sqrt(113), which is the absolute value of your vector, written as |v|. Now, to express the vector in the form (|v|cosθ, |v|sinθ), we need to find the angle θ. This is found using the arctangent function (also known as the inverse tangent or atan). θ = atan(y/x), where x and y are the x and y components of your vector respectively. Be careful with the sign as atan can only return values from -π/2 to π/2.

In your case θ = atan(8/-7), but since this gives a negative answer and the vector is in the second quadrant where angles are positive, you should add π to your result to get the correct angle. Then you can substitute |v| and θ into the expressions for the x and y components.

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Jasmine finished the bike trail in 2.5 hours at an average rate of 2.5 miles per hour.Lucy biked the same trail at a rate of 6 1/5 mile per hour.How long did it take lucy to bike the trail?

Answers

2.5 hours at a rate of 2.5 miles per hour = 2.5 * 2.5 = 6.25 miles

the trail was 6.25 miles long

Lucy rode at 6 1/5 mile per hour

 so 6.25 / 6 1/5 = 1.008 = 1.01 hours

two pounds of peaches cost 4.50 5 pounds cost 11.25and 10 pounds cost 22.50 what is the constant of proportionality

Answers

4.50 /2 = 2.25

11.25/5 = 2.25

22.50/10 = 2.25

 the constant is the price per pound which is 2.25

Answer:

c

Step-by-step explanation:

What is the area of a triangle with verticies at (-2,1), (2,1) and (3,4)

Answers

check the picture below.

notice, is just a triangle with a base of 4, and an altitude of 3.

I need help with this question... phenobarbital elixir contains 2 grams in 1 liter of elixir. How many milligrams of phenobarbital are contained in 1 teaspoon of elixir?

Answers

Answer:

9.86 milligrams

Step-by-step explanation:

It is given that 1 liter f elixir contains 2 grams of phenobarbital elixir.

Since 202.884 teaspoons = 1 liter

so 1 teaspoon of elixir =  [tex]\frac{1}{202.884}[/tex] liter

∵ 1 liter of elixir contains phenobarbital = 2 gms.

∴  [tex]\frac{1}{202.884}[/tex] liter of elixir contains phenobarbital =  [tex]\frac{2*1}{202.884}[/tex] = 0.009858 grams

or 0.009858 × 10³ milligrams

 = 9.86 milligrams.

Therefore, 9.86 milligrams of phenobarbital will be required.

Final answer:

The milligrams of phenobarbital in one teaspoon of elixir, multiply the milligrams per milliliter (2 mg/mL) by the volume of one teaspoon (5 mL), resulting in 10 milligrams per teaspoon.

Explanation:

The milligrams of phenobarbital in one teaspoon of elixir by first understanding the concentration of the solution and then using the volume conversion. Since 1 liter of the phenobarbital elixir contains 2 grams (2000 mg), we need to find out how many milligrams are contained in a smaller volume, specifically in one teaspoon, which is 5 milliliters. milligrams, so 2 grams = 2000 milligrams.

Next, consider the volume conversion: There are 1000 milliliters in 1 liter. So if 2000 mg is in 1000 milliliters, there would be 2 mg in 1 milliliter (since 2000 ÷ 1000 = 2).

Finally, since 1 teaspoon equals 5 milliliters, we multiply the amount of milligrams in 1 milliliter by 5.

Mathematically: 2 mg/mL * 5 mL = 10 mg

Therefore, there are 10 milligrams of phenobarbital in 1 teaspoon of elixir.

What is the area of 30 X 40 rectangle in square units

Answers

1,200 square units.
this is because 30x40= 1,200.

The area of the given rectangle is 1200 square units.

Given that, width = 30 units and length = 40 units.

What is the area of a rectangle?

The formula of the area of a rectangle is used to find the area occupied by the rectangle within its boundary. The area of a rectangle is obtained by multiplying its length and width. Thus, the formula for the area, 'A' of a rectangle whose length and width are 'l' and 'w' respectively is the product "l × w".

Now, the area of a rectangle = 40 × 30

= 1200 square units

Therefore, the area of the given rectangle is 1200 square units.

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Calculate the mean of the number set 5 10 12 4 6 11 13 5

Answers

For calculating the mean, you want to add up all of the numbers then divide by how many numbers there are. So you'd do:

5+10+12+4+6+11+13+5 then divide that by 8

The answer to your question is: 8.25

When the expression -5x^2+20x-17 is written in the form $a(x+d)^2+e$, where a, d, and e are constants, then what is the sum a+d+e?



PLEEEASE HELP

Answers

Solution by completing the square.

-5x^2+20x-17
=-5(x^2-4x)-17
=(-5(x-2)^2+20) -17
=-5(x-2)^2+3
So a=-5, d=-2, e=+3
a+d+e=-5-2+3=-4

what 3 digits are in the units period?

Answers

I am in the fith grade so trust me if you don't know the answer it is ones,tens,and hundreds

Describe the set of all points p(x,y) in a coordinate plane that satisfy the given condition

Answers

Part A:

The line x = -2 is a vertical line passing through point (-2, 0) on the x axis.

The set of points satisfying x = -2 are all the points on the coordinate plane which lies on the vertical line crossing point -2 on the x-axis.



Part B:

The line y = 5 is a horizontal line passing through point (0, 5) on the y axis.

The set of points satisfying y = 5 are all the points on the coordinate plane which lies on the horizontal line crossing point 5 on the y-axis.



Part C:

The line x = 0 is the y axis.

The set of points satisfying x ≥ 0 are all the points on the coordinate plane to the right of the y-axis.



Part D:

The set of points satisfying xy > 0 are all the points on the coordinate plane which lies on the 1st quadrant and all the points on the coordinate plane which lies on the 3rd quadrant.



Part E:

The line y = 0 is the x axis.

The set of points satisfying y < 0 are all the points on the coordinate plane that are below the x-axis.



Part F:

The line x = 0 is the y axis.

The set of points satisfying x = 0 are all the points on the coordinate plane that lie on the y-axis.



Part G:

The line y = -2 is a horizontal line passing through point (0, -2) on the x axis.

The set of points satisfying y = -2 are all the points on the coordinate plane which lies on the horizontal line crossing point -2 on the y-axis.



Part H:

The line x = 4 is a vertical line passing through point (4, 0) on the x axis.

The set of points satisfying x = 4 are all the points on the coordinate plane which lies on the vertical line crossing point 4 on the x-axis.



Part I:

The set of points satisfying x / y < 0 are all the points on the coordinate plane which lies on the 2nd quadrant and all the points on the coordinate plane which lies on the 4th quadrant.



Part J:

The line xy = 0 are the x-axis and the y-axis.

Therefore, the set of points satisfying xy = 0 are all the points on the coordinate plane which lies on the x-axis and all the points on the coordinate plane which lies on the y-axis.



Part K:

The line y = 1 is a horizontal line passing through point (0, 1) on the y axis.

The set of points satisfying y > 1 are all the points on the coordinate plane which lies above the horizontal line crossing point 1 on the y-axis.



Part L:

The line y = 0 is the x axis.

The set of points satisfying y = 0 are all the points on the coordinate plane that lie on the x-axis.
Final answer:

The set of all points p(x,y) in a coordinate plane that satisfy the given condition refers to the graph that represents the change of y as a function of x.

Explanation:

In a rectangular (Cartesian) xy-coordinate system, a point in a plane is described by a pair of coordinates (x, y). The set of all points p(x,y) that satisfy the given condition refers to the plotted or sketched graph that represents the change of y as a function of x. Using the given table of points (1,5), (2,10), (3,7), and (4,14), we can plot these points on a graph and connect them to see how y values change with different x values.

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At a speed of 45 yards per minute, a 120 pound swimmer burns 420 calories per hour and a 172 pound swimmer burns 600 calories per hour. write an equation that models the number of calories burned per hour as a function of the swimmer's weight.

Answers

c = w*45/13 + 60/13 I will be assuming that the equation will be linear since there are only 2 data points available. The form of the equation will be c = aw + b where c = calories burned a = some constant w = weight b = some other constant. If you look at the equation, you'll notice that it looks like the equation for a line i slope intercept form. So first, let's calculate the slope of the desired equation. a = (600-420)/(172-120) = 180/52 = 45/13 = 3.461538462 Now we have the equation c = w*45/13 + b Substitute the values for a known point, giving 420 = 120*45/13 + b Now solve for b 420 = 120*45/13 + b 420 = 5400/13 + b 420 - 5400/13 = b 5460/13 - 5400/13 = b 60/13 = b So now the equation is c = w*45/13 + 60/13

Kristina invests $5,000 at 15% simple interest for 2 years.How much interest did Kristina earn over the 2 years?

Answers

using
SI = PRT/100
=( 5000 × 15 × 2)/100
= 50×15×2= 1500$

then difference between the cubes of two numbers is twice the value of the perfect square of a possitive Intiger

Answers

There are many solutions. But what do you mean with a perfect square of a number. I thought a number IS a perfect square or not.

For example, the difference between 2² and 4² = 12, which is twice the number 6, which is √36

The difference between 2² and 6² = 32, which is twice the number 16, which is a perfect square.

So choose depending on your interpretation of the question... ;-)

Write a problem saying a single load of laundry cost $2 and a double load costs $4 the machine only accept quarters what is the answer

Answers

The problem is: A laundromat charges $2 for a single load of laundry and $4 for a double load. The machine only accepts quarters. How many quarters are needed to wash two double loads of laundry?

To solve this problem, we first need to determine the total cost of washing two double loads. Since each double load costs $4, two double loads will cost 2 * $4 = $8.

Next, we need to determine how many quarters are in $8. Since there are 4 quarters in a dollar, there are 4 * 8

= 32 quarters in $8.

Therefore, 32 quarters are needed to wash two double loads of laundry

What number is 1/10 greater than 7962

Answers

792.6
just divide the number by 1/10


792.6 
just divide the number by 1/10

Matrix's van holds 14 gallons of gas and can be driven 25 miles per gallon. His next road trip is 1,050 miles away. How many times will his ban need to be filled up to make the trip?

Answers

so Matrix's van can take up to 14 gallons of gasoline, and it does 25 miles for one gallon, wait a second, it takes up 14 gallons though, if it does 25 miles for 1 gallon, how much does it do for the whole 14 gallons?  well, 14 * 25, that many miles for a whole full tank.

On his next trip, he'll be driving it for 1050 miles, how many tanks is that?

well, how many times does (14*25) go into 1050?   1050/(14*25)  that many.

Simplyfy (x - 5 / x^3 + 27) + (2 / x^2 - 9)

Answers

The answer simplified should be x-5/x^3+18+2/x^2. Hope that is helpful.
[tex]\bf \textit{difference of squares} \\ \quad \\ (a-b)(a+b) = a^2-b^2\qquad \qquad a^2-b^2 = (a-b)(a+b)\\ \quad \\ \textit{difference of cubes} \\ \quad \\ a^3+b^3 = (a+b)(a^2-ab+b^2)\qquad (a+b)(a^2-ab+b^2)= a^3+b^3 \\\\ -------------------------------\\\\[/tex]

[tex]\bf \cfrac{x-5}{x^3+27}+\cfrac{2}{x^2-9}\implies \cfrac{x-5}{x^3+3^3}+\cfrac{2}{x^2-3^2} \\\\\\ \cfrac{x-5}{(x+3)(x^2-3x+3^2)}+\cfrac{2}{(x-3)(x+3)}\\\\\\ \cfrac{x-5}{(x+3)(x^2-3x+9)}+\cfrac{2}{(x-3)(x+3)} \\\\\\ \textit{so, we'll use the LCD of }(x-3)(x+3)(x^2-3x+9) \\\\\\ \cfrac{(x-3)(x-5)~~+~~(x^2-3x+9)2}{(x-3)(x+3)(x^2-3x+9)} \\\\\\ \cfrac{x^2-8x+15~~+~~2x^2-6x+18}{(x-3)(x+3)(x^2-3x+9)}\implies \cfrac{3x^2-14x+33}{(x-3)(x+3)(x^2-3x+9)}[/tex]

What is the meaning of the function of h = f(50, t)? describe the behavior of this function?

Answers

Dependent variable h depends upon two independent variaables, one of which is represented by 50 and the other by the letter t.  In other words, h is a function of two variables.  Without further detail it is impossible to describe the behavior of this function h=f(50,t).

Suppose that h = f(x,t) = 2x - 1/t.  This is my invention.

Then f(50,t) would come out as 2(50) - 1/t, which is a function of just 1 variable.


−4x−y+4 when x=−1/4 and y=3 .

Answers

-4(-1/4)-(3)+4
1 - 3 + 4
-2 + 4
2

n=6x35+4 what does n represent in a division problem

Answers

 answer is 214 - n = 214

If the test for a disease is accurate 65% of the time, how often will it come back positive if a patient doesn't have the disease?

Answers

Answer:

35% of the time

Step-by-step explanation:

A P E X

Which of the following symbols correctly completes this comparison? 5 + 10 + 13 ? 13 + 10 + 5 = < > ≠

Answers

The answer is =, because in addition, it doesn't matter what order you add things in, it comes out the same.

The correct symbol to complete the expression is,

⇒ 5 + 10 + 13 = 13 + 10 + 5

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The expression is,

⇒ 5 + 10 + 13 ? 13 + 10 + 5

Now,

Since, The expression is,

⇒ 5 + 10 + 13 ? 13 + 10 + 5

From LHS;

⇒ 5 + 10 + 13 = 28

From RHS;

⇒ 13 + 10 + 5 = 28

So, We get;

The correct symbol to use is,

⇒ 5 + 10 + 13 = 13 + 10 + 5

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How does the throughput of pci express version 3.0 compare to pcie version 2.0?

Answers

PCI(e) version 3.0 has a throughput twice as fast as that of its predecessor. Version 2.0 had a maximum throughput of 16Gb/second, while version 3.0 increased the maximum theoretical speed to 32Gb per second. This allows for much faster data transfer when using objects like solid state hard drives and ethernet cards.
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