how to calculate rational numbers ​

Answer:

Step-by-step explanation:

[tex] \sf{Given}[/tex]

[tex] \sf{hypotenuse = 5}[/tex]

[tex] \sf{base = 2.1}[/tex]

[tex] \sf{perpendicular = x}[/tex]

Now, Let's find the value of x

Using Pythagoras theorem

[tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]

Plug the values

⇒[tex] \sf{ {5}^{2} = {x}^{2} + {2.1}^{2} }[/tex]

Evaluate the power

⇒[tex] \sf{25 = {x}^{2} + 4.41}[/tex]

Swap the sides of the equation

⇒[tex] \sf{ {x}^{2} + 4.41 = 25}[/tex]

Move constant to R.H.S and change it's sign

⇒[tex] \sf{ {x}^{2} = 25 - 4.41}[/tex]

Calculate the difference

⇒[tex] \sf{ {x}^{2} = 20.59}[/tex]

Squaring on both sides

⇒[tex] \sf{x = 4.54}[/tex]

Hope I helped!

Best regards!!

Answer: Hi!

The value of the variable is 11.

The angles will be equal, as the lines intersect and make an X. To find the value of the angle, we would first subtract 2 from 35 and then divide by 3 to fill in the expression.

35 - 2 = 33

33 ÷ 3 = 11

The value of x is 11.

Hope this helps!

Answer:

16m²

25m²

9m²

Step-by-step explanation:

4 × 4 = 16m²

5 × 5 = 15m²

3 × 3 = 9m²

Mike: From the school to the mall, we could count out 16 units. From the mall to the library, we could count out 29 units. When we add 16 and 29, we get the distance Mike traveled: 45 units.

Henry: He traveled from the school to the library. To find out how long this distance is, we look at our previous numbers. From the school to the mall: 16. From the mall to the library: 29

To solve, we need to know the Pythagorean Theorem. We use the formula a^2 + b^2 = c^2. Here, 16 is a and 29 is b. We need to square both numbers and add them together to get c^2.

[tex]16^2=256\\29^2=841\\256+841=1097\\1097=c^2[/tex]

Then, we have to square 1097 to find c.

√1097 ≈ 33

Total: We subtract Henry's distance from Mike's to get our final answer.

45 - 33 = 12

Mike traveled 12 more units than Henry.

===========================================

Plug in x = 0

f(x) = 2x^2 + 5

f(0) = 2(0)^2 + 5

f(0) = 5

Plug in x = 2

f(x) = 2x^2 + 5

f(2) = 2(2)^2 + 5

f(2) = 13

Now use the formula below to find the average rate of change (AROC) from x = a to x = b

AROC = ( f(b) - f(a) )/( b-a )

AROC = ( f(2) - f(0) )/( 2-0 )

AROC = ( 13 - 5 )/( 2 - 0)

AROC = 8/2

AROC = 4

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

This is the same as finding the slope of the line through (0,5) and (2,13)

m = (y2 - y1)/(x2 - x1)

m = (13-5)/(2-0)

m = 8/2

m = 4

Answer:

Student Ticket: $8

Adult $28

Step-by-step explanation:

To find out the price of each ticket create 2 equations, then solve for x & y

x = student tickets

y = adult tickets

25x + 28y = 984

25x + 25y = 900

To do this first put x on one side of the equation

25x = 900 - 25y

x = 36 - y

Now substitute this equation in x for the first equation

25(36 - y) + 28y = 984

Now distribute 25 in 36 - y, 900 - 25y + 28y = 984

After this combine like term, then subtract 900 from each side, 3y = 84

Then divide 3 on each side, y = 28

Lastly substitute 28 for y in any equation to solve for x, x = 8

x & y are the price of each ticket

Answer:D

Step-by-step explanation:

Answer:

x - 1 a n d - 2 x ^ 2 - 9 x - 7

Answer:

7

Step-by-step explanation:

h,n

m,n

n,o

j,k

k,l

k,i

Answer:

[tex]2xy-5xz+x[/tex]

Step-by-step explanation:

I'm going to assume you wanted to multiply these terms.

To do this, we distribute [tex]x[/tex] into each term in the parentheses.

[tex]2y \cdot x = 2xy\\\\-5x \cdot x = -5xz\\\\1 \cdot x = x[/tex]

Combining these terms, we get [tex]2xy-5xz+x[/tex].

Hope this helped!

Answer:

12.5 kilograms

Step-by-step explanation:

Given:

Half of the granola served with breakfast.

Let the amount of Granola present initially = [tex]x[/tex] kg

Half of it ([tex]\frac{x}{2}[/tex]) served with breakfast, so remaining granola :

[tex]x-\dfrac{x}{2} = \dfrac{x}{2}[/tex]

After dinner, the remaining granola 6,250 gm granola was served with yogurt dessert.

First of all, let us convert it to kilogram because the answer is required in Kilograms.

We know that:

1000 gms = 1 kilograms

1 gms = 0.001 kilograms

6250 gms  = 6250 [tex]\times[/tex] 0.001 = 6.250 kilograms

Now, as per given question statement:

[tex]\dfrac{x}{2} = 6.250\ kg\\\Rightarrow x = 2 \times 6.250\\\Rightarrow \bold{x = 12.5\ kg}[/tex]

So, the answer is:

Girl scout camp started with 12.5 Kilograms of granola.

Answer:

8 hours 37.

800x8= 6400

800x 0.5 (or 30 mins) = 400

6400+400= 6800

one 5th of an hour = 12 minutes.

Answer:

Below

Step-by-step explanation:

The end behavior of a function is how it grows when it reaches both plus and - infinity.

To do that we will calculate:

● lim h(x) x=> +infinity = lim-4x+4 x=> +inf = lim -4x x=> +inf

-4 is negative so the limit will be -infinity

● lim (-4x+4) x=> -inf = lim (-4x) x=> -inf

-4 is negative, x is negative then -4x is positive. So the limit will be + inf

Answer:

the 3'd power

Step-by-step explanation:

4x4=16 16x4=64

Answer:

[tex]\Huge \boxed{\mathrm{3}}[/tex]

Step-by-step explanation:

Let the power be x.

[tex]\mathrm{4^x=64}[/tex]

Take log of both sides.

[tex]\mathrm{log(4^x)=log(64)}[/tex]

[tex]\mathrm{x \cdot log(4)=log(64)}[/tex]

Divide both sides by log(4).

[tex]\displaystyle \mathrm{x=\frac{log(64)}{log(4)} }[/tex]

[tex]\mathrm{x=3}[/tex]

Answer:

y= ½ x + 5

Step-by-step explanation:

[tex] (-4,3) \: (6,8). \\ x_1 = - 4 \\ y_1 = 3 \\ x_2 = 6[/tex]

[tex]y_2 = 8 \\ \frac{y - y_1}{x - x_1} = \frac{y_2 -y_1}{x_2 - x_1} [/tex]

[tex] \frac{y - 3}{x - ( - 4)} = \frac{8 - 3}{6 - ( - 4)} = \frac{y - 3}{x + 4} = \frac{5}{10} [/tex]

[tex]10(y - 3) = 5(x + 4) \\ 10y - 30 = 5x + 20 \: \\ 10y = 5x + 20 + 30 = 10y = 5x + 50 \\ [/tex]

[tex] \frac{10y}{10} = \frac{5}{10} x + \frac{50}{10} \\ y = \frac{1}{2} x + 5[/tex]

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of the line can be written as y = (1/2)x+5.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is the y-intercept.

To write the equation of the line, we need to firstly find the slope of the equation. Therefore, the slope of the equation can be written as,

Slope = (8 -3)/[6 - (-4)] = 5/10 = 1/2

Now, substitute the value of the slope and the any point in the general equation of a line. Therefore, we can write,

y = mx + c

8 = (1/2)(6) + C

8 = 3 + C

C = 5

Hence, the equation of the line can be written as y = (1/2)x+5.

Learn more about Equation of Line:

https://brainly.com/question/21511618

#SPJ5

So in this case "number" will be "x"

Triple means multiply by 3 = 3x

1 less means minus 1.

3x-1

Answer:

Amna is the fastest typist.

Step-by-step explanation:

Amna = 710 words/15 minutes = 47.3 words per minute

Sara = 810 words/18 minutes = 45 words per minute

Uzma = 780 words/20 minutes = 39 words per minute

Answer:

[tex]P(T_1\ n\ T_2) = \frac{2}{21}[/tex]

Step-by-step explanation:

From the comments in your question; we have

Stars = 4

Triangles = 5

Circles = 3

Squares = 3

Required  

Determine the probability of both shapes being triangles

First, calculate the total

[tex]Total = 4 + 5 + 3 + 3[/tex]

[tex]Total = 15[/tex]

Next, calculate the probability of the first selected shape being a triangle;

P(T₁) = Number of triangles divided by total number of shapes

[tex]P(T_1) = \frac{5}{15}[/tex]

[tex]P(T_1) = \frac{1}{3}[/tex]

Next, calculate the probability of the second selected shape being a triangle;

P(T₂) = Number of triangles divided by total number of shapes

Because it's probability without replacement. the number of triangle left is 4 and the number of shapes left is 14;

So:

[tex]P(T_2) = \frac{4}{14}[/tex]

[tex]P(T_2) = \frac{2}{7}[/tex]

Hence:

[tex]P(T_1\ n\ T_2) = P(T_1) * P(T_2)[/tex]

[tex]P(T_1\ n\ T_2) = \frac{1}{3} * \frac{2}{7}[/tex]

[tex]P(T_1\ n\ T_2) = \frac{2}{21}[/tex]

Hence, the required probability is [tex]\frac{2}{21}[/tex]

Answer:

2/21

Step-by-step explanation:

There are 4 stars, 5 triangles, 3 circles, and 3 squares

For the first drawing there are 5 triangles and a total of 15 shapes.

p(first triangle) = 5/15 = 1/3

Since there is no replacement, for the second drawing, and one triangle has been taken, now there are 4 triangles left and 14 total shapes left.

p(second triangle) = 4/14 = 2/7

p(two triangles) = p(first triangle) * p(second triangle)

p(two triangles) = 1/3 * 2/7

p(two triangles) = 2/21

Answer: Light blue

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]2\$ on \:each \:game\\10\$ on food\\Let \:x \:be the \:no \:of \:games \:he \:plays\\\\2x +10\\Must\: be \:less\: than\: or \:equal \:to\: 25\$\\\\= 2x+10\:\le 25[/tex]

====================================================

Explanation:

Add the minutes for now

55 minutes + 10 minutes = 65 minutes = 60 minutes + 5 minutes = 1 hour, 5 minutes

The minute portions add to 1 hour, 5 minutes. The hour portions add to 3+1 = 4.

Add on the "1 hour, 5 minute" portion and we get 5 hours, 5 minutes

This is the total duration of the round trip hike. Keep in mind that this does not include any time spent with Jennifer resting at the top of the mountain. This time duration assumes that once she gets to the top, she pretty much starts the hike back down the mountain.

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

Now convert 3:45 PM to military time. We add 12 hours to get 15:45

Subtract off 5 minutes to get 15:40

Then subtract off 5 hours to get 10:40, which converts back to 12-hour time notation to be 10:40 AM

Answer:

$3 Each

Step-by-step explanation:

27 Spent Toatal.

Soft Drink for 3.

27-3 = 24

He bought eight candy bars, so divide 24 by 8.

24/8 = 3

So each was 3 dollars.

Answer:

Answer C: Reflecting over the line y = x

Step-by-step explanation:

A function and its inverse have always symmetry around the line y = x (called also the identity line)

Therefore answer C seems to be the only answer that addresses such.

Answer:

-1/8

Step-by-step explanation:

Convert 1/4 into 2/8.

Then, minus -3/8 and 2/8

Answer:

-3/8 + 1/4 = 1/8

Step-by-step explanation:

-3/8 + 1/4

1/4 = 2/8

then:

2/8 - 3/8 = -1/8

Answer:

1. 7.5 hours

2. TV

3. Computer

4. All electronic usage except for the heater would decrease because summer is usually when people go outside and don't really stay indoors. While in winter, most people stay inside their houses.

Answer:

[tex]tan(A) = \frac{2\sqrt{15}}{11}[/tex]

Step-by-step explanation:

Given:

Right ∆ABC

AB = 61

BC = 60

AC = 11

Required:

Value of tan A in radical form

SOLUTION:

[tex] tan(A) = \frac{opposite}{adjacent} [/tex]

Opposite = 60

Adjacent = 11

[tex] tan(A) = \frac{60}{11} [/tex]

[tex] tan(A) = \frac{\sqrt{4*15}}{11} [/tex]

[tex]tan(A) = \frac{2\sqrt{15}}{11}[/tex]

Step-by-step explanation:

It is given that,

A 2-liter bottle of juice costs $2.80.

It means that 1 liter bottle of juice costs $1.4.

A box containing six 12-liter bottles sells for $3.90.  

(6×12)l i.e. 72 liter bottles sells for $3.9

1 liter bottles sells for $0.05416

It is clear that "A box containing six 12-liter bottles sells for $3.90." have higher cost per liter. Its cost is $0.05416 per liter. Hence, the correct option is (D).

Answer:

D

Step-by-step explanation:

Greetings from Brasil...

Rewriting the problem sets

A = {-7, 4, 2, 14, 21, 34, 42}

B = {...; 2; 4; 6; 8; 10; 12; 14; 16; 18; 20; 22; 24; 26; 28; 30; 32; 34; 36; 38; 40; 42;...}

C = {...; -14; -7; 0; 7; 14; 21; 28; 35; 42; 49; 56; 63; 70; 77;...}

So, according to the statement, it is desired:

A ∩ B ∩ C - the intersection between the 3 sets, that is, which numbers are present simultaneously in the 3 sets....

Looking at the sets we conclude that

Answer:

5     3

6     4

4     2

Step-by-step explanation:

Answer:

[tex]y=-\frac{2}{3}x+12[/tex]

Step-by-step explanation:

Step 1: Rule out answers

The answer cannot be B or D because the y-intercept is at 12(b = 12) and in a linear equation y=mx+b, b is the y intercept.

B has the y intercept at 18

D has the y intercept at 18

Step 2: Find the slope

The slop is the change in y over the change in x.  We can also write this as [tex]\frac{rise}{run}[/tex]

We see it lowers by 2 so we will put -2 as the numerator

We also the x value increase by 3 every time it gets lowered by 2 so the run is 3

Therefore the slope is [tex]-\frac{2}{3}[/tex]

Step 3: Plug in the the variables to get the linear equation

[tex]y=mx+b[/tex]

[tex]y=-\frac{2}{3}x+12[/tex]

Therefore the answer is A. [tex]y=-\frac{2}{3}x+12[/tex]

Answer:

[tex]\Large \boxed{{y=-\frac{2}{3}x +12}}[/tex]

Step-by-step explanation:

y = mx + b (slope-intercept form of a line)

m is slope

b is y-intercept

The y-intercept of the line is (0, 12) or 12.

y = mx + 12

The slope of the line can be found through rise over run.

(0, 12) and (18, 0) are two points on the line.

m = (y2-y1)/(x2-x1)

m = (0-12)/(18-0)

m = -12/18

m = -2/3

The slope of the line is -2/3.

y = -2/3x + 12

Answer:

(-4+8) ÷ 2 = 2

uuujhhhhh

Answer:

x = {-5, -⅓}

Step-by-step explanation:

[tex]3 {x}^{2} + 16x + 5 = 0[/tex]

[tex]3 {x}^{2} + 15x + x + 5 = 0[/tex]

[tex]3x(x + 5) + 1(x + 5) = 0[/tex]

[tex](x + 5)(3x + 1) = 0[/tex]

[tex]x = - 5 \: or \: - \frac{1}{3} [/tex]

[tex]x = \{ - 5 \: , - \frac{1}{3} \}[/tex]