What is an equation of the line that passes through the point (4, -1) and has
slope -5?
This is what my teacher says to do and i dont know how to solve it. Can anyone help?

Answer:

Step-by-step explanation:

h(x) - j(x) => [tex]x^2-(2x^2-5)[/tex]

The negative sign out in front of the set of parenthesis changes the signs of everything inside the parenthesis, so now we have, without parenthesis:

[tex]x^2-2x^2+5[/tex] which simplifies down to

[tex]-x^2+5[/tex]

Step-by-step explanation:

Given the equation

[tex]3x^3\:+10x^2-x-12=0[/tex]

Steps

[tex]3x^3+10x^2-x-12[/tex]

Rational Root Theorem definition

[tex]\mathrm{For\:a\:polynomial\:equation\:with\:integer\:coefficients:\quad }a_nx^n+a_{n-1}x^{n-1}+\ldots +a_0[/tex]

[tex]\mathrm{If\:}a_0\mathrm{\:and\:}a_n\mathrm{\:are\:integers,\:then\:if\:there\:is\:a\:rational\:solution}[/tex]

[tex]it\:could\:be\:found\:by\:checking\:all\:the\:numbers\:produced\:for\:\pm \frac{dividers\:of\:a_0}{dividers\:of\:a_n}[/tex]

[tex]a_0=12,\:\quad a_n=3[/tex]

[tex]\mathrm{The\:dividers\:of\:}a_0:\quad 1,\:2,\:3,\:4,\:6,\:12,\:\quad \mathrm{The\:dividers\:of\:}a_n:\quad 1,\:3[/tex]

[tex]\mathrm{The\:following\:rational\:numbers\:are\:candidate\:roots:}\quad \pm \frac{1,\:2,\:3,\:4,\:6,\:12}{1,\:3}[/tex]

Plugging x = -1 is False

[tex]3\left(-1\right)^3+10\left(-1\right)^2-\left(-1\right)-12=0[/tex]

[tex]-4=0[/tex]    ∵L.H.S ≠ R.H.S

Plugging x = 1 is True

[tex]3\cdot \:1^3+10\cdot \:1^2-1-12=0[/tex]

[tex]0=0[/tex]      ∵ L.H.S = R.H.S

Similarly,

x = -2 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = 2 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = -3 satisfies the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

As

[tex]3\left(-3\right)^3+10\left(-3\right)^2-\left(-3\right)-12=0[/tex]

[tex]0=0[/tex]       ∵ L.H.S = R.H.S

x = 3 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = 4 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = -4 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = 6 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = -6 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = -12 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = 12 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = -1/3 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = 1/3 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = -2/3 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = 2/3 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = -4/3 satisfies the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

As

[tex]3\left(-\frac{4}{3}\right)^3+10\left(-\frac{4}{3}\right)^2-\left(-\frac{4}{3}\right)-12=0[/tex]      ∵ L.H.S = R.H.S  

x = 4/3 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = -2 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = 2 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = -4 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = 4 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

Hence, out of all the mentioned rational roots of the equation [tex]3x^3\:+10x^2-x-12=0[/tex], the rational roots which validate the equation are [tex]x=-\frac{4}{3},\:x=1,\:x=-3[/tex].

Keywords: rational roots, rational root theorem

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Final answer:

The Peace of Augsburg allowed rulers to establish either Lutheranism or Roman Catholicism as the official religion in their lands, giving birth to the principle 'whose realm, their religion' but excluded other religious groups such as Calvinists and Anabaptists.

Explanation:

The religious settlement reached with the Peace of Augsburg in 1555 allowed rulers within the Holy Roman Empire to choose either Lutheranism or Roman Catholicism as the official religion of their territories. This principle, known as cuius regio, eius religio ('whose realm, their religion'), meant that a ruler's subjects were obliged to follow the same religion.

The Peace of Augsburg formally recognized the division between Catholics and Protestants, mainly Lutherans, and ended the religious conflict within the empire at that time. However, other religious groups, such as Calvinists and Anabaptists, were not accommodated, and the agreement failed to resolve underlying tensions leading to future wars, including the devastating Thirty Years' War.

The final concentration of salicylic acid in the ointment is approximately 8.70%.

To calculate the final concentration of salicylic acid in the ointment base, we need to know the total mass of the product after mixing. The final concentration of salicylic acid is expressed as a percentage, which is the mass of salicylic acid divided by the total mass of the product, multiplied by 100.

Let's assume that when you add 8 g of salicylic acid to 84 g of the ointment base, there is no change in the total volume, and the two substances mix completely.

Total mass of the product = Mass of salicylic acid + Mass of ointment base

Total mass = 8 g + 84 g = 92 g

Now, we can calculate the final concentration of salicylic acid:

Final Concentration (%) = (Mass of salicylic acid / Total mass) * 100

Final Concentration (%) = (8 g / 92 g) * 100 ≈ 8.70%

So, the final concentration of salicylic acid in the ointment is approximately 8.70%.

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Answer:  0.85

Step-by-step explanation:

step 1   0.3572928 / 0.419

             count the number of figures yo have after the decimal  point.

After counting , multiply both the numerator and the denominator

10000000 to make the whole expression a whole number for easy division.

   we now      0.3572928                 10000000

                     ------------------       x        ---------------

                         0.419                         10000000

           =         3572928

                    ----------------

                      4190000

         =           0.8527

        Now to two decimal places

              = 0.85

The slope is -4/5

Step-by-step explanation:

We have to observe the graph to find two points to find slope.

The graph has two points

(-5,0) and (0, -4)

The formula for slope is given by:

[tex]m = \frac{y_2-y_1}{x_2-x_1}\\[/tex]

Here

(x1,y1) = (-5,0)

(x2,y2) = (0,-4)

Putting the values

[tex]m = \frac{-4-0}{0+5}\\=-\frac{4}{5}[/tex]

Hence,

The slope is -4/5

Keywords: slope, steepness

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Answer: point, line, and plane.

Step-by-step explanation:

Answer:

Hope it helps In Geometry, we have several undefined terms: point, line and plane. From these three undefined terms, all other terms in Geometry can be defined.  A line is defined as something that extends infinitely in either direction but has no width and is one dimensional while a plane extends infinitely in two dimensions.

Step-by-step explanation:

Final answer:

The fraction of a 3-gallon container filled with 1/3 gallon of water is 1/9. This is found by dividing the amount of water by the total capacity of the container. It can be represented through multiplication and division, both yielding the result 1/9.

Explanation:

The question asks what fraction of a container is filled if there is 1/3 gallon of water in a 3-gallon container. To represent this situation, we can simply realize that the fraction filled is equal to the amount of water in the container (1/3 gallon) divided by the container's total capacity (3 gallons).

So, 1/9 of the container is filled with water.

To set up a multiplication and division equation to represent the situation:

These representations show how to derive the fraction of the container that is filled using multiplication and division.

Answer:

  3. (x, y) = (3, 2)

  6. (x, y) = (10, 4/3)

  9. (x, y) = (-2, -1)

  12. (x, y) = (8, 3)

Step-by-step explanation:

3, 6. See the attachment. 3 is graphed in red/orange. 6 is graphed in blue, purple.

__

9. Use the expression for y in the second equation to substitute for y in the first equation:

  4(3x +5) -x = -2

  12x +20 -x = -2 . . . eliminate parentheses

  11x = -22 . . . . . . . .  subtract 20, collect terms

  x = -2 . . . . . . . . . . . divide by 11

  y = 3(-2) +5 = -1 . . .substitute for x in the second equation

The solution is (x, y) = (-2, -1).

__

12. Subtract 3/4x from the second equation to get an expression for y:

  y = 9 - 3/4x

Substitute that into the first equation:

  3(9 -3/4x) -5/4x = -1

  27 -9/4x -5/4x = -1 . . . . eliminate parentheses

  -14/4x = -28 . . . . . . . . . . collect terms, subtract 27

  x = 8 . . . . . . . . . . . . . . . . multiply by -4/14

  y = 9 -3/4(8) = 3 . . . . . . substitute into the expression for y

The solution is (x, y) = (8, 3).

Answer:

OPTION A: [tex]$ \frac{12}{1 + 8x} $[/tex], where [tex]$ x \ne - \frac{1}{8} $[/tex].

Step-by-step explanation:

Given: [tex]$ \frac{- 12x^4}{x^4 + 8x^5} $[/tex]

Taking [tex]$ x^4 $[/tex] common outside in the denominator, we get:

[tex]$ = \frac{-12x^4}{(x^4)(1 + 8x)} $[/tex]

[tex]$ x^4 $[/tex] will get cancelled on the numerator and denominator, we get:

[tex]$ = \frac{-12}{1 + 8x} $[/tex]

we know that the denominator can not be zero.

That means, 1 + 8x [tex]$ \ne $[/tex] 0.

[tex]$ \implies 8x \ne -1 $[/tex]

[tex]$ \implies x \ne \frac{-1}{8} $[/tex]

So, the answer is: [tex]$ \frac{-12}{1 + 8x} $[/tex], where [tex]$ x \ne \frac{-1}{8} $[/tex].

Answer:

par value of the TIPS is $1034.05

Step-by-step explanation:

Given:

-  original reference CPI = 182.1

- current CPI = 188.3

Assume face value of tips = $1000

par value of the TIPS = [tex]face\ value\ of\ tips\times \frac{current\ CPI}{original\ reference\ CPI}[/tex]

par value of the TIPS = [tex]1000\times \frac{188.3}{182.1}\approx $1034.05[/tex]

Final answer:

The par value of a TIPS adjusts with the CPI's inflation rate. To find the adjusted par value of a 4.15% TIPS, multiply the original par value by 1 plus the inflation rate, which is determined by the percentage increase from the original to the current CPI.

Explanation:

A student asked about the par value of a Treasury Inflation-Protected Security (TIPS) given an original reference Consumer Price Index (CPI) of 182.1 and a current CPI of 188.3. The par value of TIPS adjusts with inflation to protect investors, with the adjustment based on the change in the CPI.

First, we need to calculate the percentage increase in the CPI by using the formula:

(Current CPI - Original CPI) ÷ Original CPI x 100%.

Plugging in the given CPI values:

(188.3 - 182.1) ÷ 182.1 = 0.0340 or 3.40%

This percentage tells us how much the CPI has increased since the TIPS was issued. To find the adjusted par value, you would multiply the original par value of the TIPS (which is typically $1,000) by 1 plus the inflation rate. Since we do not have the original par value, we can only provide the formula for its calculation.

The adjusted par value would be:

Original Par Value x (1 + Inflation Rate).

Answer:

AY = 10 cm.

Step-by-step explanation:

Given that, ΔABC is similar to ΔAXY

and [tex]\frac{AB}{AX }  = \frac{5}{3}[/tex]

⇒  [tex]\frac{AC}{AY }  =  [tex]\frac{BC}{XY } = \frac{5}{3}[/tex]

⇒ BC = XY× \frac{5}{3}[/tex] =  \frac{20}{3}[/tex] (as XY = 4 cm given)

Now, check the attached figure,

given, BY bisects ∠XYC

let ∠XYB = ∠BYC = x

⇒ ∠AYX = 180-2x (angle on a straight line)

and also ∠AYX = ACB (similar triangle properties)

⇒ ∠ACB = 180-2x

Now, sum of angles in ΔBYC = 180°

⇒ ∠YBC = x

⇒ BC = YC (as two sides of equal angles are equal in a triangle)

⇒ YC =  \frac{20}{3}[/tex]

And also [tex]\frac{AC}{AY }  = \frac{5}{3}[/tex]

AC = AY + YC

⇒ [tex]\frac{AY+YC}{AY }  = \frac{5}{3}[/tex]

⇒ [tex]\frac{AY+\frac{20}{3}[/tex]}{AY }  = \frac{5}{3}[/tex]

⇒ 5AY = 3AY + 20

⇒ AY = 10 cm

Answer:

8X2-38X-380

Step-by-step explanation:

(2x+10)(4x-38)

Expand the brackets.

2X(4X-38)+10(4X-38)

Multiple the inner ones by the outer ones

(2X)(4X)-(38)(2X)+(10)(4X)-(10)(38)

=> 8X2-78X+40X-380

8X2-38X-380

Answer:

the most it could cost would be $83 dollars

Step-by-step explanation:

2000-1500=500

500/3=83.33

Answer:

Two options for this case will be,

Clockwise rotation : -90°

Anti-Clockwise rotation : +270°

Step-by-step explanation:

If we rotate the triangle clockwise -90° then the vertex will be at (5,0).

Similarly by rotatating it anti-clockwise for +270° it will be at same position

Answer:

C.) D.)

Step-by-step explanation:

Answer:

[tex]\displaystyle 2x - 3y = 6\:OR\:y = \frac{2}{3}x - 2 \\ \\ 3x - 2y = 40\:OR\:y = \frac{3}{2}x - 20[/tex]

Step-by-step explanation:

2 = ⅔[6] + b

4

[tex]\displaystyle -2 = b \\ \\ y = \frac{2}{3}x - 2[/tex]

If you want it in Standard Form:

y = ⅔x - 2

- ⅔x - ⅔x

_________

−⅔x + y = −2 [We do not want fractions in our standard equation, so multiply by the denominator to get rid it.]

−3[−⅔x + y = −2]

[tex]\displaystyle 2x - 3y = 6[/tex]

_______________________________________________

−5 = 3⁄2[10] + b

15

[tex]\displaystyle -20 = b \\ \\ y = \frac{3}{2}x - 20[/tex]

If you want it in Standard Form:

y = 3⁄2x - 20

- 3⁄2x - 3⁄2x

__________

−3⁄2x + y = −20 [We do not want fractions in our standard equation, so multiply by the denominator to get rid of it.]

−2[−3⁄2x + y = −20]

[tex]\displaystyle 3x - 2y = 40[/tex]

* Parallel Lines have SIMILAR RATE OF CHANGES [SLOPES], so ⅔ and 3⁄2 remain the way they are.

I am joyous to assist you anytime.

The equilibrium price 'p' is found when setting the supply and demand equations equal to each other and solving for p. Doing so gives us p = 29, which is not available among the provided options, suggesting an error in the question or answer options.

In the given situation, the point of equilibrium occurs when the quantity demanded (D) is equal to the quantity supplied (S). Therefore, we can set the demand equation equal to the supply equation and solve for p.

The equations at the moment are: D = p + 22 and S = 3p - 36.

Setting them equal to each other means setting D and S to the same value, resulting in: p + 22 = 3p – 36.

To solve for p, you first combine like terms, which will give you: 22 + 36 = 3p - p, simplifying that leads to: 58 = 2p.

Finally, to isolate p, divide both sides of the equation by 2: p = 58 / 2 = 29.

However, none of the options includes p = 29, which suggests there might be a typo or error in the provided choices or the equations.

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Answer: x = 12

Step-by-step explanation:

[tex]\frac{6}{x}[/tex] = [tex]\frac{4}{8}[/tex]

cross multiply

4x = 6 × 8

4x = 48

divide through by 4

x = 12

Answer:

B. 28 degrees

Step-by-step explanation:

ok so,

the starting temperature is 35 degrees then the temperature dropped 4 degrees. making the temp 31 degrees. next the temperature rose 2 degrees, making it 33 degrees. lastly, the temperature dropped another 5 degrees making it 28 degrees out on wednesday.  

so the number line showing this would be B.

Final answer:

After a cold front caused the temperature to drop by 40 degrees from the initial 35 degrees Fahrenheit, the resulting temperature would be -5 degrees Fahrenheit on the number line for Wednesday morning at 8:00am.

Explanation:

The student originally observed a temperature of 35 degrees Fahrenheit on Sunday morning. If we suppose a cold front blows in and drops the temperature by 40.0 Fahrenheit degrees, the temperature change can be calculated by subtracting 40 from the initial temperature:

35 °F - 40 °F = -5 °F

Therefore, the number line that shows the temperature on Wednesday morning at 8:00am should have a point at -5 degrees Fahrenheit, representing the new temperature after the cold front.

Answer:

The height of the aquarium is [tex]33.75\ in[/tex]

Step-by-step explanation:

Remember that

[tex]1\ gal=231\ in^3[/tex]

[tex]1\ ft=12\ in[/tex]

we know that

The volume of a rectangular prism is equal to

[tex]V=LWH[/tex]

In this problem we have

[tex]V=1,000\ gal=1,000(231)=231,000\ in^3[/tex]

so

[tex]231,000=LWH[/tex] ----> equation A

[tex]L=W+1(12)[/tex] ---> [tex]W=L-12[/tex]  --->equation B (convert ft to in)

[tex]H=L-4.6(12)[/tex]--->[tex]H=L-55.2[/tex] ---> equation C (convert ft to in)  

substitute equation B and equation C in equation A

[tex]231,000=L(L-12)(L-55.2)[/tex]

solve for L

Apply distributive property

[tex]231,000=(L^2-12L)(L-55.2)[/tex]

[tex]231,000=L^3-55.2L^2-12L^2+662.4L[/tex]

[tex]L^3-67.2L^2+662.4L-231,000=0[/tex]

Solve the cubic equation by graphing

using a graphing tool

The solution is L=88.95 in

see the attached figure

Find the height of the aquarium H

[tex]H=L-55.2[/tex]

substitute the value of L

[tex]H=88.95-55.2=33.75\ in[/tex]

Find the value of W  

[tex]W=88.95-12=76.95\ in[/tex]

Answer:

30%

Step-by-step explanation:

Use formula to find percent decrease

[tex]\text{Percent Decrease}=\dfrac{\text{Old Value}-\text{New Value}}{\text{Old Value}}\cdot 100\%[/tex]

In your case,

Old Value = 2.5 pounds

New Value = 1.75 pounds

Hence,

[tex]\text{Percent Decrease}=\dfrac{2.5-1.75}{2.5}\cdot 100\%\\ \\=\dfrac{0.75}{2.5}\cdot 100\%\\ \\=\dfrac{75}{250}\cdot 100\%\\ \\=\dfrac{3}{10}\cdot 100\%\\ \\=30\%[/tex]

Answer:

y = 3

Step-by-step explanation:

Assumption:

Something is missing in question. If we see deeply it is apparent that there is some issue with option b i.e. B) 8 − 4x 10 = 4 + 2x we assume that the questioner want to type B) 8-4x^10 = 4 + 2x.

Answer:

The correct answer is B) 8-4x^10 = 4 + 2x.

Step-by-step explanation:

All equations given is the question can be solve easily to determine the value of x. However if we solve equation mentioned in option b we cannot  get single answer easily.

For example value of x in eq given in option A

15x + 123 = 5x+4

1oX = -119

 X = -119/10

Answer:

The answer is d

Step-by-step explanation:

i just did it lol

The probability of drawing the 8 of spades from a deck of cards is 1/52, or approximately 0.0192, which can also be expressed as 1.92%.

The probability of drawing the 8 of spades from a deck of cards is calculated as the number of favorable outcomes divided by the total number of possible outcomes. In this case, there is only 1 8 of spades card in the deck, and there are a total of 52 cards. Therefore, the probability is 1/52, or approximately 0.0192, which can also be expressed as 1.92%.

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Answer:

7^9

Step-by-step explanation:

When dealing with exponents inside and outside parenthesis with only one term in the parenthesis, you multiply the exponents. By doing this, you get 7^3x3, which is 7^9

Answer:

40353607 or 7^9

Step-by-step explanation:

7 to the third power is 343

343 to the third power is 40353607 :)

But the exponents times each other equal nine. This will be your answer: 7^9

Answer:

[tex]S=42000*\sum_{i=0}^{n}0.02^n[/tex]

Step-by-step explanation:

The salary per year is the combination of the $42000 per year (constant) plus the 2% rise per year. So the ecuation is:

Firt year [tex]S=(42000 + 0.02*42000)[/tex]

Second year [tex]S=(42000 + 0.02*42000)+0.02*(42000 + 0.2*42000)[/tex]

Generalizing:

[tex]S=42000*\sum_{i=0}^{n}0.02^n[/tex]

Final answer:

The equation that represents Giovanna's current situation is Current Salary = $42,840.

Explanation:

The equation that represents Giovanna's current situation can be determined by using the formula for calculating annual salary with a percentage increase.

The formula is:
Current Salary = Initial Salary + (Percentage Increase * Initial Salary)

Using this formula, we can substitute the given values:
Initial Salary = $42,000
Percentage Increase = 2% (or 0.02)

Substituting these values into the formula:

Current Salary = $42,000 + (0.02 * $42,000)

Simplifying the equation:

Current Salary = $42,000 + $840

Current Salary = $42,840

Therefore, the equation that represents Giovanna's current situation is:
Current Salary = $42,840

Answer:

[tex]\large\boxed{16a^6x^4y^2}[/tex]

Step-by-step explanation:

[tex]\text{Use}\\\\(ab)^n=a^nb^n\\\\(a^n)^m=a^{nm}\\=====================\\\\\left(-4x^2ya^3\right)^2=\\\\=(-4)^2(x^2)^2(y)^2(a^3)^2\\\\=(-4)(-4)x^{2\cdot2}y^2a^{3\cdot2}\\\\=16x^4y^2a^6[/tex]

The expression (−4x^2ya^3)^2 written as a monomial in standard form is 16x^4y^2a^6.

To write the given expression, (−4x2ya3)2, as a monomial in standard form, we first need to calculate square ofeach part of the term inside the parentheses. The square of -4 is 16. The rule of exponents states that when raising a power to a power, you multiply the exponents. Therefore, the square of x2 is x4 (since 2*2=4), the square of y is y2, and the square of a3 is a6 (since 3*2=6). Combining these, we find that the expression in standard form is 16x4y2a6.

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Answer:

Option C) 24 < x < 54

Step-by-step explanation:

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

Let

x ----> the measure of the third side

Applying the triangle inequality theorem

1) [tex]15+39 > x[/tex]

[tex]54 > x[/tex]

Rewrite

[tex]x < 54\ units[/tex]

2) [tex]x+15> 39[/tex]

[tex]x > 39-15[/tex]

[tex]x > 24\ units[/tex]

therefore

The range of possible measures for the third side is the interval (24,54)