Solve the following system of equations using the elimination method. 8x – 5y = 5 –8x – 6y = 6 Question 3 options: A) (0,1) B) (0,–1) C) (2,–3) D) (–2,3)

let's firstly convert the mixed fractions to improper fractions and then divide them.

[tex]\stackrel{mixed}{4\frac{2}{3}}\implies \cfrac{4\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{14}{3}} ~\hfill \stackrel{mixed}{1\frac{5}{9}}\implies \cfrac{1\cdot 9+5}{9}\implies \stackrel{improper}{\cfrac{14}{9}} \\\\[-0.35em] ~\dotfill\\\\ -\cfrac{14}{3}\div\cfrac{14}{9}\implies -\cfrac{~~\begin{matrix} 14 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{3}\cdot \cfrac{9}{~~\begin{matrix} 14 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies -\cfrac{9}{3}\implies -3[/tex]

Answer:

-3

Step-by-step explanation:

Lets convert 4 2/3 to an improper fraction

-(4 * 3/3 + 2/3)/1 5/9

Combine 4 and 3/3

-(4 * 3/3 + 2/3)/1 5/9

Combine numerator over denom

-4 * 3 + 2/3/1 5/9

Simplify numerator

-12 + 2/3/1 5/9

Add 12 and 2

-14/3/1 5/9

Now we convert 1 5/9 to an improper.

-14/3/(9/9) + (5/9)

Combine

-14/3/(9 + 5)/9

Add 9 and 5

-14/3/(14/9)

Multiply yhe numerator by the reciprocal of the denom

-14/3 * 9/14

14(-1)/3 * 9/14

-1/3 * 9

Cancel the common factor of 3

-1/3 * (3(3))

-1 * 3 = -3

The expression, (6x - 2) - (-x + 5), is simplified as 7x - 7. The student's error was wrong calculation in the final steps where he subtracted 2 from 5.

A simplified expression is an expression that is evaluated to its simplest form, that is, it cannot be simplified further.

Given:

(6x - 2) - (-x + 5)

Open the bracket by multiplying each of the terms in (-x + 5) by the negative sign (-):

6x - 2 + x - 5

Combine like terms

7x - 7

Thus, the expression, (6x - 2) - (-x + 5), is simplified as 7x - 7. The student's error was wrong calculation in the final steps where he subtracted 2 from 5.

Learn more about simplified expressions on:

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Here mark the angles

By using angle sum property

So

So

Answer:

IH < GI < GH < FH < FG

Step-by-step explanation:

Find missing angles

Sum of interior angles of a triangle = 180°

⇒ ∠GFH = 180 - 55 - 75 = 50°

⇒ ∠IGH = 180 - 59 - 63 = 58°

Side lengths in relation to interior angles

The longest side of a triangle is opposite the largest interior angle, and the shortest side is opposite the smallest angle.

Therefore, angles/sides in order of least to greatest:

ΔIGH

∠IGH = 58  →   its opposite side is IH

∠GHI = 59  →   its opposite side is GI

∠G|H = 63  →   its opposite side is GH

Therefore,  IH < GI < GH

ΔFGH

∠GFH = 50  →  its opposite side is GH

∠FGH = 55  →   its opposite side is FH

∠FHG = 75  →   its opposite side is FG

Therefore, GH < FH < FG

Combining:  IH < GI < GH < FH < FG

Answer:

100 ft

Step-by-step explanation:

1 yd = 3 ft

Gena: 12 yd= 36 ft

Alicia: 10 yd and 4 ft= 34 ft

Lyona: about 10 yd= 30 ft

36 + 34 + 30 = 100

Answer:

6 1/2

Step-by-step explanation:

i don't know the rest but I know that that one might be 6 1/2

Answer:

Step-by-step explanation:

[tex] \frac{5}{ {3b}^{3} - {2b}^{2} - 5 } = \frac{2}{ {b}^{3} - 2 } \\ 5( {b}^{3} - 2) = 2( {3b}^{3} - {2b}^{2} - 5) \\ {5b}^{3} - 10 = {6b}^{3} - {4b}^{2} - 10 \\ 10 - 10 = {6b}^{3} - {5b}^{3} - {4b}^{2} \\ 0 = {b}^{3} - {4b}^{2} \\ 0 = {b}^{2} (b - 4) \\ [/tex]

b = 0 or b - 4 = 0

b = 0

b = 4

[tex]\tt v=\dfrac{d}{t}[/tex]

[tex]\tt t=\dfrac{d}{v}=\dfrac{169.6}{53}=3.2~h[/tex]

Answer:

Step-by-step explanation:

Let x represent the width of the garden. Then its length is 3x-1 and its area is ...

  A = LW . . . . . . . . . . . . area of a rectangle is length times width

  A = (3x -1)(x) = 150

  3x^2 -x = 150

  x^2 -1/3x +1/36 = 50 +1/36 . . . . divide by 3 and complete the square

  x -1/6 = √(50+1/36) . . . . . . . . . take the square root

  x = (1 +√1801)/6 ≈ 7.2397 . . . width of Chanda's garden

The length will be ...

  3x -1 = 3(1 +√1801)/6 -1 = (1 +√1801)/2 -1 = (-1 +√1801)/2 ≈ 20.7191

To the nearest tenth meter, the garden is 20.7 m long and 7.2 m wide.

Step-by-step explanation:

hope it helps,plss correct me if im wrong

Answer:
5y + 2

Step-by-step explanation:

5 - 2y + 7y - 2 - 1

5 - 2 - 1 - 2y + 7y

2 + 5y

Hope it helps ⚜

Answer:

The exponent is different from each other. One exponent is 3/4 and the other is 2/4. These make the value different.

Step-by-step explanation:

Answer:

c = ?

j = 13 bottles

c × j = $9.23

c = $9.23 ÷ j

= $9.23 ÷ 13

= $0.71 / 71 cents

Answer:

$0.71

Step-by-step explanation:

If c x j = $9.23 and j is 13, then c is  $9.23/13

$9.23/13 = $0.71

=$0.71

Answer:

n = -13

Step-by-step explanation:

38 = -2n + 12

Subtracting 12 from both sides:

==> 38 - 12 = -2n + 12 - 12

==> 26 = -2n

multiplying both sides by (-1):

==> -26 = 2n

dividing both sides by 2:

==> -13 = n

Answer:

Step-by-step explanation:

38 = -2n + 12

26 = -2n

n = 26 : (-2)

n = -13

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

check

38 = -2 * (-13) + 12

38 = 26 + 12

38 = 38

the answer is good

Answer:

32 quarts

Step-by-step explanation:

1 gallon = 4 quarts

⇒ 8 gallons = 8 x 4 = 32 quarts

Answer:

32 quarts

Step-by-step explanation:

Khan

Answer:

(4x + 3)(4x - 3)

Step-by-step explanation:

I am going to assume by 16x2 -9 you mean 16x² - 9

     The factorization means the factors are "broken" up. If you multiply them together, we will reach 16x² - 9 again.

     First, we can look at factors of 9. This gives us 1, 3, and 9. We will use 3. Since the nine is negative, one will be + 3 and one will be - 3 since a negative times a positive is a negative.

(   + 3)(   - 3)

     Last we can factor the 16x² portion. I know that 4 times 4 is 16, and 4x times 4x is 16x².

(4x + 3)(4x - 3)

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.

- Heather

Answer:

1/3

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

Seems like the pattern is adding and then subtracting the next square number up:

7 + 4 = 11

11 - 9 = 2

2 + 16 = 18

so 18 - 25 = -7 is the next number

Answer:

-12

Step-by-step explanation:

-10 + (-2)

-10 - 2

Answer: -12

Answer:

-12is the answer,hope it will help you.

[tex]=-10+(-2)\\=-10-2\\=-12[/tex]

Answer:

a

Step-by-step explanation:

a square +b square equals to c Square

therefore

2. 2 2

a + b = c

Answer:(a) getting the equation:

We'll assume that the altitude is represented by the x-axis and that the boiling point is represented by the y-axis.

Therefore, we have two given points:

(8400 , 200.4) and (4200 , 206.7)

Since the relation is linear, therefore, the graph forms of straight line with the general equation:

y = mx + c where m is the slope and c is the y-intercept.

First, we will calculate the slope:

m = (y2-y1) / (x2-x1) = (206.7 - 200.4) / (4200 - 8400) = -0.0015

Therefore, the equation of the line now is:

y = -0.0015x + c

Then, we will need to calculate the y-intercept. In order to do so, we will use any give point and substitute in the previously obtained equation as follows:

y = -0.0015x + c

206.7 = -0.0015(4200) + c

c = 213

Based on the above calculations, the equation of the line is:

y = -0.0015x + 213

(b) getting the boiling point at altitude = 2100 ft:

Now, in order to calculate the boiling point at altitude 2100, we will substitute in the equation of the line as follows:

y = -0.0015(2100) + 213 = 209.85 degrees Fahrenheit

Step-by-step explanation:

Answer:

x= 21/4

Step-by-step explanation:

1- Convert the expressions

5 ( x - 3 3/4 ) = 7 1/2

2- Remove the parentheses

5 ( x - 15/4 ) = 15/2

3- Move the constant to the right

5x - 75/4 = 15/2

4- Calculate the sum

5x = 15/2 + 75/4

5- Divide both sides

5x = 15/2 + 75/4

[tex]36-b ^ { 2 } -c ^ { 2 } +2bc\\= 36-\left(b^{2}+c^{2}-2bc\right) \\= 6^{2}-\left(b-c\right)^{2} \\=\boxed{ \left(6-b+c\right)\left(6+b-c\right) }[/tex]

Hope it helps ⚜

Answer:

C or 260.48

Step-by-step explanation:

Find area of both triangles:

20*16/2/2*2=160

Find area of circle;

pi*r*r/2= area of circle

d/2=r

16/2=8

pi*8*8/2 is about 100.53

160+100.53=260.53

1. Observe problem

2. Plug in values

|-54|+30=

54+30=

84

Answer:

21 in. squared

Step-by-step explanation:

Answer:

Multiplying the lines and the cost.

Step-by-step explanation:

35$ times 6 is 210. 25$ times 6 is 150. This is the cost of both companies.

Answer:

R330

Step-by-step explanation:

2 + 3 = 5

5x = 825

2x = 825 x 2/5

825 x 2 = 1650

1650/5 = 330

Mandy makes R330.

Mandy's share from the profit is R495

Data;

This is the portion shared between two or more entities in a definite proportion.

To find Mandy's share, let's add 2 and 3 and then take the fraction of 3/5 and multiply it by the profit made.

[tex]2 + 3 = 5\\\frac{3}{5} * 825 = 495[/tex]

Mandy's share from the profit is R495

Learn more on ratio here;

https://brainly.com/question/2914376