Add or subtract each fraction

2 + 15/8

Answer:

  a) x = -2

  b) 8 integer values

Step-by-step explanation:

Matthew's solution is correct as far as it goes. However, he failed to take into account the possibility of negative square roots.

His solution might rightly look like ...

  3 < 3x² ≤ 75

  1 < x² ≤ 25 . . . . . divide by 3

  1 < ±x ≤ 5 . . . . . . take the square root

Separating the results:

  1 < x ≤ 5

  -1 > x ≥ -5 . . . . . . multiply by -1

The value x=-2 shows Matthew's solution is incorrect:

  3 < 3(-2)² ≤ 25   ⇒   3 < 12 ≤ 25 . . . true

__

x can have the integer values {-5, -4, -3, -2, 2, 3, 4, 5}, a total of 8 values.

__

In the attached, the white space (and dashed line) are the solution set. The shaded areas (and solid line) are excluded from the solution set.

_____

Additional comment

It can be helpful to remember that ...

  [tex]\sqrt{x^2}=|\,x|\ne x[/tex]

That is, values of x may be negative, but the positive square root will only show you a positive value.

Answer:

y = 2

Step-by-step explanation:

Given equations:

x+y=7

x = 5 .........given that x is 5

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

5 + y = 7  ...............replace x as 5 here.

y = 7 - 5

y = 2

Answer:

a

Step-by-step explanation:

a square +b square equals to c Square

therefore

2. 2 2

a + b = c

Answer:

21 in. squared

Step-by-step explanation:

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:

-10 1/2

Step-by-step explanation:

-2 2/5 times 4 3/8

Turn fractions into mixed numbers: -12/5 and 35/8

Cross multiply: -12/5 times 35/8= 21/2

Turn fraction back into proper fraction: -10 1/2

Answer:

1/3

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:

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:

2x2x2x7 is 56, 2^2x3x7 is 84, and 2x2x2x13 is 104.

Step-by-step explanation:

Answer:

-The graph crosses the y-axis at the point (0,0)

None of the given options is correct

A graph crosses the y-axis at the point (0,y).This means that the graph will cross the y-axis when x-=0

To find the point where the graph crosses the y-axis,substitute x=0 into the given equation y-9x

substitute x=0 into the equation y-9x to find the corresponding value of y

That is,

y=9(0)

y=0

therefore the graph crosses the y-axis at the point (0,0)

Step-by-step explanation:

hope it hlps

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:

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

Answer:

Step-by-step explanation:

Given,

A camel drinks water in 10 minutes = 15 gallons

So,

Water drank by the camel in 1 minute = [tex]\frac{15}{10} gallon[/tex]

So, Water drank by the camel in 6 minutes

= ( [tex]\frac{15}{10}[/tex] × 6) gallons

= 1.5 × 6 gallons

= 9 gallons

Hence,

Amount of water drank by the camel in 6 minutes is 9 gallons of water. (Ans)

Answer:

total area: 141 in²

Step-by-step explanation:

area of the figure: area of two triangles together + area of trapezium

area of the figure: 1/2 * base * height + 1/2 * ( a + b ) * height

area of the figure: 1/2 * 6 * 8 + 1/2 * ( 10 + 16 ) * 9

area of the figure: 24 + 117

area of the figure: 141 in²

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

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:

513.954016

Step-by-step explanation:

If what you mean was (6^5/7^3)^2 than:

(6^5/7^3)^2 is equal around 513.954016

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:

-8

Step-by-step explanation:

136/-17 when simplified because -10-7=-17 then plug into a calculator and you get -8

Hope this helps! :)

Answer:

Step-by-step explanation:

Step-by-step explanation:

hope it helps,plss correct me if im wrong

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

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

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:

https://brainly.com/question/25802006

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:

-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:

75 feet per second to feet per minute is 4500

Step-by-step explanation:

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

1. Observe problem

2. Plug in values

|-54|+30=

54+30=

84