This box plot shows information about the marks scored in a test.

Nobody gained exactly 30, 48 or 70 marks.
120 students gained less than 70 marks.
How many students gained more than 48 marks?

The difference in distance between Aero plane A and B is; 34.67 km

To get the bearing;

∠H = (115 - 90) + (270 - 203)

∠H = 92°

Then, we will use cosine rule to get the distance between both Planes A and B.

d_ab = √(18² + 29² - 2(18 * 29) * cos 92)

d_ab = √(324 + 841 + 36.435)

d_ab = 34.67 km

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Number Line:

Closed Circles are used when signs are "≤" or "≥"

Open Circles are used when signs are "<" or ">"

The graph of x > -1 on a number line would be towards the right from -1 with open circle as the sign is ">"

Graph should look like this:

Answer:

D

Step-by-step explanation:

7.50/10=0.75

0.75*6=4.5

So, you will get 6 batteries for $4.50 which of course is less than $4.95.

The greasiest possible number of intersections for these graphs is 2 if the Mark is solving an equation where one side is a quadratic expression and the other side is a linear expression.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

As we know the standard form of a quadratic equation is:

[tex]\rm Y = \rm ax^2+bx+c[/tex]

And a linear equation can be written as:

y = mx + d

Equating both the expression:

ax² + bx + c = mx + d

ax² + (b-m)x + c - d = 0

The above equation is an also quadratic equation, and we know that the quadratic equation have maximum two roots.

Thus, the greasiest possible number of intersections for these graphs is 2 if the Mark is solving an equation where one side is a quadratic expression and the other side is a linear expression.

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Answer:

x = 55.866 ft.

Step-by-step explanation:

39^2 + 40^2 = x^2

1521 + 1600 = 3121

sqrt(3121) = 55.8659

Rounded = 55.866

Make sure to add the ft.

Answer:

Step-by-step explanation:

a²+b²=c²

39²+40²=c²

3121=c²

c=√3121

c=55.866 to 3.d.p

Answer:

20cm²

Step-by-step explanation:

3+3=6, 4+1=5 (make it a rectangle and find the sides first)

A=6×5=30cm²

Now you can take away the invisible sides,

30-6-3-1=20

Answer:

He can print 62 documents

Step-by-step explanation:

500/8=62.5

He can print only 62 documents because he cannot print half a document.

Hope this helps!

If not, I am sorry.

The equation x = 7 - 4√3 is a radical expression, and the value of the radical expression is [tex](x + \frac 1x)^2 = 3650401 -2107560\sqrt 3[/tex]

The equation is given as:

x = 7 - 4√3

So, we have:

[tex](x + \frac 1x)^2 = (7 - 4\sqrt 3 + \frac{1}{7 - 4\sqrt 3})^2[/tex]

Take the LCM

[tex](x + \frac 1x)^2 = (\frac{49 -56\sqrt3 + 48}{7 - 4\sqrt 3})^2[/tex]

Evaluate the like terms

[tex](x + \frac 1x)^2 = (\frac{97 -56\sqrt3 }{7 - 4\sqrt 3})^2[/tex]

Rationalize

[tex](x + \frac 1x)^2 = (\frac{(97 -56\sqrt3)(7 - 4\sqrt 3) }{49 -48})^2[/tex]

Evaluate the difference

[tex](x + \frac 1x)^2 = ((97 -56\sqrt3)(7 - 4\sqrt 3))^2[/tex]

Expand

[tex](x + \frac 1x)^2 = (679 -388\sqrt 3 -392\sqrt 3 + 672)^2[/tex]

Evaluate the like terms

[tex](x + \frac 1x)^2 = (1351 -780\sqrt 3 )^2[/tex]

Expand

[tex](x + \frac 1x)^2 = 1825201 +1825200 -2107560\sqrt 3[/tex]

[tex](x + \frac 1x)^2 = 3650401 -2107560\sqrt 3[/tex]

Hence, the value of the radical expression is [tex](x + \frac 1x)^2 = 3650401 -2107560\sqrt 3[/tex]

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The number of small tiles are needed​ is 300 tiles.

Using area of rectangular formula

Area of the room = length(l) × breadth (b)

Area of the room=300 cm×180 cm

Area of the room=54,000 cm²

Number of tiles needed = Area of rectangular region / Area of one tile

Number of tiles needed=54,000/180

Number of tiles needed=300 tiles

Therefore the number of small tiles are needed​ is 300 tiles.

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The quadratic functions are given as below:-

x = 3y² - 6y + 5

y = 2x² + 2

y = 2x² -8x + 6

y = 5x² + 45x -8

The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.

As we know that the function which will have the highest power of the variable equal to 2 will be called a quadratic polynomial.

So from the given expressions following equations has a degree of 2.

x = 3y² - 6y + 5

y = 2x² + 2

y = 2x² -8x + 6

y = 5x² + 45x -8

Therefore the above equations are quadratic functions.

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Answer:

  0.86°

Step-by-step explanation:

The relations between trig functions and sides of a right triangle are summarized in the mnemonic SOH CAH TOA. It tells you the relation between an angle and its adjacent and opposite sides is ...

  Tan = Opposite/Adjacent

__

The geometry described in the problem statement is modeled by the right triangle shown in the attachment. (The horizontal scale has been compressed.) The angle of interest has an adjacent side of 400 ft. Its opposite side is the additional elevation the ball must have to clear the fence (8 ft - 2 ft) = 6 ft.

For angle α, we have the relation ...

  tan(α) = (6 ft)/(400 ft) = 0.015

The inverse tangent function can be used to find the angle from its tangent:

  α = arctan(0.015) ≈ 0.859372°

The angle of elevation needs to be a minimum of 0.86°.

The value of the expression f(5) + j(-2)  is -8 where f(x)=12-3x and j(x)=x² + 4x - 1

The expression is given as:

f(5) + j(-2)

Where f(x)=12-3x and j(x)=x² + 4x - 1

Calculate f(5) and j(-2)

f(5)= 12 - 3(5) = -3

j(-2) = (-2)² + 4(-2) - 1 = -5

So, we have:

f(5) + j(-2)  = -3 - 5

Evaluate

f(5) + j(-2)  = -8

Hence, the value of the expression f(5) + j(-2)  is -8

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Answer:

B. (2, 4)

Explanation:

Given equations:

a) y = x + 2

b) y = 3x – 2

Solve them simultaneously:

x + 2 = 3x – 2

x - 3x = -2 - 2

-2x = -4

x = 2

Then find y = x + 2 = 2 + 2 = 4

Solution: (x, y) = (2, 4)

Answer:

(2,4)

Step-by-step explanation:

substitute the value of y x+2 = 3x-2

solve the value of x  x = 2

substitue the value of x into one of the equations y = 2+2

solve for y value y = 4

The slope of the  line passing through the points (3, 3) and (0, -6) is 3.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

We need to find the slope of line passing through points (3, 3) and (0, -6)

Plug in the values in formula.

m=-6-3/0-3

m=-9/-3

m=3

Hence, the slope of the  line passing through the points (3, 3) and (0, -6) is 3.

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Answer:

4x(2x-1)

Step-by-step explanation:

Using GCF, you can be able to take out a factor of 4x from 8x^2 and 4x.

Answer:

x= 67, y= 113 , z= 67........... ...........

Answer:

[tex]\overline{TH}[/tex]

Step-by-step explanation:

The diameter of a circle is a line that goes from one side to the other in a circle. It is the longest straight line that can be drawn in a circle. It also goes through the center of a circle.

That is the answer

- Kan Academy Advance

Answer:

k=36; y=1.44; x=8

Step-by-step explanation:

a) y= k/square root of x

9=k/square root of 16

9=k/4

9×4= (k/4)×4

therefore k=36

b) Using k...

y=36/25

therefore y=1.44

c) 4.5=36/x

4.5×(x)= (36/x)×(x)

4.5x=36

therefore x=8

Answer:

Correct option is C)

given, y≥2x+1 and

y>

2

1

x−1

Answer:

D

Step-by-step explanation:

y>_2/3 x+1 (as diagram shows the deepest line that's why it should be either greater than or equal sign or less than or equal sign)

Now check those point,

we get for (-3,-1) is -1=-1 and for (3,3) is 3=3. This can be greater than bcoz it's upon the root point.

Answer:

a=263.76cm3

b=301.44cm3

c=41.52m3

Answer:

  total: $86.68

Step-by-step explanation:

The value of each change is found by multiplying the base amount by the percentage change. The result is rounded to the nearest cent. Here, we're applying 3 changes. In order to make sure they're rounded properly, we need to apply them in order

__

The discount amount is ...

  discount = bill × 10% = $75.00 × 0.10 = $7.50

The discounted amount is ...

  bill - discount = $75.00 -7.50 = $67.50

__

The tax amount is ...

  tax = discounted bill × tax rate = $67.50 × 0.07 = $4.725 ≈ $4.73

The bill with tax added is ...

  discounted bill + tax = $67.50 +4.73 = $72.23

__

The tip is apparently added to the amount after tax, so the amount of the tip is ...

  tip = taxed bill × 0.20 = $72.23 × 0.20 = $14.446 ≈ $14.45

The bill with tax and tip added is ...

  total bill = $72.23 +14.45 = $86.68

_____

Additional comment

At each stage, the amount can be found by using the multiplying factor (1+p), where p is the percentage change. All three factors applied gives a result of ...

  75×(1-0.10)(1+0.07)(1+0.20) = 75×0.9×1.07×1.2 = 86.67

You will note this differs by a penny from the amount calculated above. That is a consequence of rounding up both the tax and the tip.

Answer:

Step-by-step explanation:

I’m not sure u didn’t even add numbers

Answer:

tanG = 2

tanH = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

The function tangent is the opposite side divided by the adjacent one(SohCahToa).

Relative to angle G, the side with measure 2 is opposite while the wide with measure 1 is adjacent. From this we can set up an equation and substitute:

tan(m<G) = [tex]\frac{opposite}{adjacent}[/tex]

tan(m<G) = [tex]\frac{2}{1} = 2[/tex]

The same can be done for <H. The opposite side is 1 while the adjacent is 2:

tan(m<H) = [tex]\frac{opposite}{adjacent}[/tex]

tan(m<H) = [tex]\frac{1}{2}[/tex]

Answer:

1st triangle: missing angle is 100

2nd triangle: missing angles are 50

3rd triangle: missing angle is 90, this is also a right triangle. The hypotenuse on this is the side length that reaches from angle 70 to 20. the other sides are legs

Step-by-step explanation:

Answer:

150

Step-by-step explanation:

The common difference, d, is +3      add +3 to find the next term.

  to find the second term add +3 to the first term

     to find the third term add  2 * +3

        to find the 60th term add  59 * +3 to the first term

                 -27  +   (59*3) = 150

Question 8 of 25

The amount of water dispensed by a water dispenser is normally distributed,

with a mean of 11.60 ounces and a standard deviation of 0.15 ounces. In

which range will the amount of water dispensed be found 95% of the time

Answer:

s

Answer:

√10+√15-√14-√21

Explanation:

(√2 * √5) = √10

(√2 * -√7) = -√14

(√3 * √5) = √15

(√3 * -√7) = -√21

Put it all together: √10 + √15 - √14 - √21

Hope this helped :)

The simplified form of the expression  (√2+√3)(√5-√7) is √10-√14+√15-√21

An expression is combination of variables, numbers and operators.

The given expression is (√2+√3)(√5-√7)

√2(√5-√7) + √3(√5-√7)

We have to apply  distributive property

√2.√5 - √2.√7 + √3.√5 -√3.√7

√2×5 -√2×7 +√3×5 -√3×7

√10-√14+√15-√21

Hence, the simplified form of the expression  (√2+√3)(√5-√7) is √10-√14+√15-√21

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