Solve this rational equation ​

We'll label the equations to keep track of what we're doing

3x+4y+4z=4    A

5x+7y+3z=5    B

4x+5y+7z=7     C

Normally in Gaussian elimination we'd pick put a constant on each equation and combine to cancel out a variable in all but one.  But here we have an opportunity to make the coefficient 1 on our variables in at least one equation.  This is a pretty good thing to do when solving these by hand.

x + y + 3z = 3         D=C-A

-2x - 3y + z = -1     E=A-B

Let's eliminate x from two equations

-y + 7z = 5          F=2D+E

-y + 5z = 5         G=4D-C

Let's eliminate y

2z = 0               H=F-G

z = 0

-y + 7z = 5

y = -5

x + y + 3z  = 3

x - 5 + 0  = 3

x = 8

Answer: (x,y,z)=(8,-5,0)

Check:

3(8)+4(-5)+4(0) = 4, good

5(8)+7(-5)+3(0)=5, good

4(8)+5(-5)+7(0)=7, good

Answer:

Its C

Step-by-step

correct edge 2021

7.5c-2.5c+8=-7

Combine the like terms:

7.5c-2.5c = 5c

Now you have 5c +8 = -7

Subtract 8 from both sides:

5c = -15

Divide both sides by 5:

c = -15/5

c = -3

Answer:

C = -3

Step-by-step explanation:

To solve this, we need to isolate the c. So we need to subtract 8 on both sides to get :

7.5c-2.5c = -15

Now combining the c's we get:

5c = -15

So c = -3

Answer:the answer is y is less than or equal to 17

Step-by-step explanation: if y + 8 is less than or equal to 25, all you have to do is subtract 8 to 25 and the answer has to be less than or equal to the number

Answer: 99.78%

Step-by-step explanation:

100% - .28 = 99.78

Final answer:

The odds against selling a car today, when the probability of selling a car is 0.28, are calculated by dividing the complement of this probability (0.72) by the original probability (0.28), resulting in odds of approximately 2.6 to 1.

Explanation:

To find the odds against selling a car today, we start with the given probability of selling a car, which is 0.28, or 28%. The probability of not selling a car, which is the complement of the given probability, is therefore 1 - 0.28 = 0.72, or 72%.

Odds can be expressed as a ratio of the probability of the event occurring to the probability of the event not occurring. In this case, the odds against selling a car are the ratio of the probability of not selling the car to the probability of selling the car:

Odds against = Probability of not selling / Probability of selling = 0.72 / 0.28 = 72/28. This ratio can be simplified by dividing both the numerator and the denominator by 28 to get the simplest form.

Thus, the simplified odds against selling a car are 2.57 : 1 (or approximately 2.6 to 1).

Answer:

(-7, 6).

Step-by-step explanation:

All sides are equal since it is a square.

The length of the side joining the first 2 points is  |-7 - 6| = 13 units and it is horizontal.

The adjacent side is vertical and also has length 13  and moves up from the last line.

So the missing coordinate has a y coordinate of  6 and an x coordinate of -7.

Answer:

x = -2 or x = -4

Step-by-step explanation:

Step 1 : Middle term break

x^2 + 6x + 8 = 0

x^2 + 4x + 2x + 8 = 0 (4+2 is equal to six and 4x2 is equal to  8)

x(x + 4) + 2(x +4)

(x+2) (x+4)

x= -2 or x= -4

!!

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\\\ ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf \left( \cfrac{4^{\frac{5}{4}}\cdot 4^{\frac{1}{4}}}{4^{\frac{1}{2}}} \right)^{\frac{1}{2}}\implies \left( \cfrac{4^{\frac{5}{4}\cdot \frac{1}{2}}\cdot 4^{\frac{1}{4}\cdot \frac{1}{2}}}{4^{\frac{1}{2}\cdot \frac{1}{2}}} \right)\implies \cfrac{4^{\frac{5}{8}}\cdot 4^{\frac{1}{8}}}{4^{\frac{1}{4}}}\implies \cfrac{4^{\frac{5}{8}+\frac{1}{8}}}{4^{\frac{1}{4}}}[/tex]

[tex]\bf \cfrac{4^{\frac{6}{8}}}{4^{\frac{1}{4}}}\implies \cfrac{4^{\frac{3}{4}}}{4^{\frac{1}{4}}}\implies 4^{\frac{3}{4}}\cdot 4^{-\frac{1}{4}}\implies 4^{\frac{3}{4}-\frac{1}{4}}\implies 4^{\frac{2}{4}}\implies 4^{\frac{1}{2}}\implies \sqrt{4}\implies 2[/tex]

Final answer:

The equivalent expression for  [tex](4^5/4 \times 4^1/4 \div 4^1/2)^1/2[/tex] is 2, found by applying properties of exponents such as multiplication, division, and power of a power.

Explanation:

The expression given is  [tex](4^5/4 \times 4^1/4) \div 4^1/2)^1/2.[/tex] To find the equivalent expression, we use the properties of exponents, which include multiplication, division, and taking a power of a power. When you multiply with the same base, you add the exponents, and when you divide, you subtract the exponents. Also, taking a power of a power means you multiply the exponents.

Following these rules:

Combine the exponents for the terms that multiply: 5/4 + 1/4 = 3/2, hence the expression simplifies to [tex]4^{(3/2)}.[/tex]

Subtract the exponent of the denominator: (3/2) - (1/2) = 1, so now we have [tex]4^1.[/tex]

Finally, apply the outer exponent of  [tex]1/2: (4^1)^{(1/2)}[/tex]which means we take the square root of 4, giving us 2 as the final answer.

Answer:

Step-by-step explanation:

You have that [tex]i^2=-1[/tex], so we must have

[tex]i^4=(i^2 )(i^2)=(-1)(-1)=1[/tex].

This says that we must make groups of four [tex]i[/tex]'s for simplify because they becomes 1, and the last group that is not of four [tex]i[/tex]'s is the result.

This is equivalent to divide 256 by 4 and use the remainder of that division, that is 0, as the new power of [tex]i[/tex], and the result is 1 because [tex]i^0 =1.[/tex]. You can see the operation:

[tex]i^{256} = (i^4)^{64}\times i^0 =1[/tex]

Answer:

A

Step-by-step explanation:

Hi again! I'm sure you will be able to solve this using the tips I gave you in your last question. Just believe in yourself and you can solve it!

I've given you the answer and you just need to tell me why!

If it's possible, I would like you to tell me why the answer is A by replying here.

Thanks and good luck!

Answer:

7/11 of the Pizza was left for Zachary.

Step-by-step explanation:

Zachary had 1 - 4/11

= 11/11 - 4 /11

= 7/11.

Final answer:

Jerome ate 4/11 of the pizza, which means that Zachary has 7/11 of the pizza left to eat after subtracting Jerome's portion from the whole pizza.

Explanation:

If Jerome ate 4/11 of the pizza, we need to determine how much is left. Since the whole pizza represents 1, or 11/11, we subtract what Jerome ate from the whole to find out what remains for Zachary. Therefore, we perform the following subtraction:

1/11 (whole pizza) - 4/11 (portion eaten by Jerome) = 7/11 (portion left for Zachary)

So, Zachary has 7/11 of the pizza left to eat.

The correct question is

 What value of b will

cause the system to have an infinite number of solutions?

For

y = 6x – b   and  -3x+(1/2)y=-3

 we have that

y = 6x – b   ---------> equation

1

-3x+(1/2)y=-3--------->  -6x+y=-6------ > -2x+y=-3------- > y=6x-6

y=6x-6------>

equation 2

 we know that

For the system to have an infinite number of solution,

equation 1 must be equal to equation 2

so

6x – b=6x-6-------> 6x-6x=b-6---------> b=6

 the answer is b=(6)

The value of b will cause the system to have an infinite number of solutions is 6

For the system of equations to have an infinite number of solutions, the system of equations must be similar

Given the system of equations:

y = 6x – b   and  -3x+(1/2)y= -3

y = 6x – b .................... 1

From the secind equation;

-3x+(1/2)y=-3

-6x+y=-6

-2x+y=-3

y=6x-6

y=6x-6

Equate with equation 1 to have:

6x - 6 = 6x - b

b = 6

Hence the value of b will cause the system to have an infinite number of solutions is 6

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its 4.8*4.1*15=295.2 cm3

Answer:

295.2 cm^3.

Step-by-step explanation:

The volume of a rectangular prism is

V = w*l*h, where w is the width, l is the long and h is the height. Then,

[tex]V = 4.1 cm * 15 cm * 4.8 cm = 295.2 cm^3[/tex].

False

why would it be true if its not.

Answer:

False

Step-by-step explanation:

Hope it helps.

Answer:

(2,5)

Step-by-step explanation:

6x+4y=32

-6x+4y=8

We will add the two equations together to eliminate x

6x+4y=32

-6x+4y=8

----------------------

      8y = 40

Divide each side by 8

8y/8 = 40/8

y = 5

Multiply the first equation by -1

-6x-4y = -32

-6x+4y=8

------------------

-12x = -24

Divide by -12

-12x/-12 = -24/-12

x = 2

Answer:

-21.79.

Step-by-step explanation:

(-10.5 + m) / 11.57 = -2.748

(-10.5 + m) = -2.748 (11.57)

-10.5 + m = -31.794

m = -31.794 + 10.5 = -21.79.

Answer:

-21.29

Step-by-step explanation:

-10.5+m/11.57=-2.748

-10.5+m=-2.748*11.57

-10.5+m=-31.79436

m=-31.79436+10.5

m=-21.29

Answer:

819.54 cm^2

Step-by-step explanation:

We are given

Slant height = l = 20cm

and

Diameter = d = 18 cm

We have to find radius first

r = d/2 = 18/2 = 9 cm

The formula for surface area is:

[tex]SA = \pi rl+\pi r^2\\= (3.14 * 9 * 20) + (3.14 * (9)^2)\\=565.5+254.34\\=819.84\ cm^2[/tex]

As second option is nearest to calculated answer, it is the correct option ..

Answer: second option.

Step-by-step explanation:

We know that we can calculate the surface area of a cone with this formula:

[tex]SA=\pi rl + \pi r^2[/tex]

Where "r" is the radius and "l" is the slant heigth.

We know that the radius is half the diameter, then the radius of this cone is:

[tex]r=\frac{18cm}{2}\\\\r=9cm[/tex]

Since we know the radius and the slant height, we can substitute values into the formula, using 3.14 for π.

Therefore, we get:

 [tex]SA=(3.14)(9cm)(20cm) + (3.14)(9cm)^2=819.54cm^2[/tex]

By multiplying, (x – 6)(5x – 4) is 5x² - 34x + 24

The process of multiplying two provided expressions made up of variables and constants is known as the multiplication of algebraic expressions. An expression that uses integer constants and variables together is called an algebraic expression.

Given

(x – 6)(5x – 4)

= 5x² - 30x -4x +24

= 5x² -34x +24

To know more about multiplication refer to :

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Answer:

She lost 3 pounds on the first week, then, the second week she gained back one pound. So in total she lost the first two weeks 2 pounds.

On each remaining week of her diet, she lost 2 pounds. So she lost 11x2 = 22. In total she lost 22pounds + 2pounds = 24 pounds,

[tex]\bf (\stackrel{x_1}{4}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-5}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-5-(-1)}{2-4}\implies \cfrac{-5+1}{-2}\implies \cfrac{-4}{-2}\implies 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-1)=2(x-4) \\\\\\ y+1=2x-8\implies y=2x-9[/tex]

Answer:

the solution is (-2, 1.67)

Step-by-step explanation:

graph both sides of the system.

find where the two libes intersect.

round to the nearest hundredth

Answer:

20

Step-by-step explanation:

5+5+5+5=20

Answer:

4 books

Step-by-step explanation:

The cost for one used = $2.27

The question requires you to find the number of books that could be purchased with $10

Let assume the cost for a single used book to be $ t

If you have $ x in your pocket then the number of books you can purchase with $ x will be;

number of books= $ x/ $t.............................(a)

Applying this expression to the question;

$t= $2.27

$ x= $10

number of books = $10/$2.27 = 4.405 = 4 books

The point slope form of this line is y+5=m(x).  Now, you need to find m (the slope) of the line using the formula (y1-y2)/(x1-x2):

(-5-4)/(0--3)

-9/3

-3

The complete point slope formula is: y+5=-3x.

Now, to fin the slope intercept form, just solve for y:

y+5=-3x

*Subtract 5 from both sides*

y=-3x-5

Hope this helps!!

Answer:

y = -3x - 5.

Step-by-step explanation:

y – y1 = m(x – x1)

The slope m =  rise /run = (4 - -5) / (-3 - 0)

= 9/-3

= -3.

Using the point (0, -5) and m =-3 in the point-slope:

y - -5 = -3(x - 0)

y + 5 = -3x

y = -3x - 5 is the required  slope-intercept form.

Answer:

Step-by-step explanation:

Y=-x^2+6x-5

Y=3

a) Use substitution :

3 = - x²+6x- 5

x²- 6x+8 = 0

b) Factor your equation:

(x- 2)(x-4)=0

c) Identify the x-values of the solutions:

x-2=0 or x-4 =0

x=2 or x=4

d) Identify the solution to the system :

x=2       y=3

      and

x=4       y=3

The nonlinear system of equations can be solved by first substituting Y=3 into the other equation, then simplifying and factoring. The solutions for x are found by setting each factor equal to zero. The overall solutions to the system are (2,3) and (4,3).

To solve the given nonlinear system of equations we can use the substitution method. The equations given are:
Y=-x^2+6x-5 and Y=3.
We can start by substituting Y=3 in the first equation, which yields:
3=-x^2+6x-5. To rewrite this equation so one side is equal to 0, follow these steps:
-x^2+6x-5-3=0.
This simplifies to:
-x^2+6x-8=0.

Next, we can factor this equation. But it will be easier to factor if we multiply through by -1:
x^2-6x+8=0.
The factors of this equation are:
(x-2)(x-4)=0.

To find the x-values of the solutions, set each factor equal to zero:
x-2=0 or x-4=0.
Solving for x, we can see that it's values are x=2 or x=4.
Hence, the solution of the system are the ordered pairs (2,3) and (4,3).

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Answer:

0.2 = 2/9

Step-by-step explanation:

Hope my answer has helped you!

Answer:

see explanation

Step-by-step explanation:

A number line with an open circle denotes > or <

A number line with a closed circle denotes ≥ or ≤

The sign of the inequality will depend on the direction of the arrow

To the right denotes > or ≥

To the left denotes < or ≤

------------------------------------------------------------------------------------------

first diagram is x > - 2

The second diagram is x ≥ - 2

The third diagram is x ≤ - 2

The fourth diagram is x < - 2

Area = Length x width and is given as square units.

The book is 1 ft x 5/8ft

Area = 1 x 5/8 = 5/8 square ft.

The answer would be D) 5/8 ft^2

Answer: the answer is 40 because 20 plus 20 equals 40

20 + 20 = 40

If you add 2 + 2 = 4 (the number values in the tens place) and 0 + 0 = 0 (the number values in the ones place). Put the 4 in tens place and 0 in the ones place which is 40

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

0.027​,1/5,23%,1/4, 0.29

Step-by-step explanation:

Please mark brainliest and have a great day!

Answer:

0

Step-by-step explanation:

To find the slope of a line given two points I just like to line up the points and subtract and then finally put 2nd difference/1st difference like this:

(-3    ,2)

(6    ,2)

----------

-9    0

2nd/1st=0/-9=0

So the slope is 0

P.S. You can also see if you plot the points you get a horizontal line after connection... Slopes of horizontal lines are 0 since slope=rise/run and there is no rise (there is zero rise)

Answer:

0

Step-by-step explanation: