maths grade 8 solution

The area of the sandbox is 5 x 5 = 25 square feet.

the cost of the sand = 25 square feet x 1.47 = $36.75

Answer: $36.75

Answer:

36.75

Step-by-step explanation:

5*5=25 ft^2

(area)

25*1.47=36.75

sand cost

Answer:

[tex]{x}^{5} + 40{x}^{4} + 640{x}^{3} + 5120 {x}^{2} + 20480{x}^{}+ 32768 [/tex]

Step-by-step explanation:

This too follows the as same process as

recall binomial theorem,

[tex] \displaystyle (a + b {)}^{n} = \sum _{k = 0} ^{n} \binom{n}{k} {a}^{n - k} {b}^{k} [/tex]

Given binomial:

comparing it to (a+b)ⁿ , we acquire:

Now substitute:

[tex] \displaystyle (x +8 {)}^{5} = \sum _{k = 0} ^{5} \binom{n}{k} {a}^{5- k} {b}^{k} [/tex]

To convert the summation into a sum, substitute the values from k=0 to k=5 into the expression which yields

[tex] \displaystyle (x + 8{)}^{5} = \binom{5}{0} {x}^{5 - 0} \cdot {8}^{0} + \binom{5}{1} {x}^{5 - 1} \cdot {8}^{1} + \binom{5}{2} {x}^{5 - 2} \cdot {8}^{2} + \binom{5}{3} {x}^{5 - 3} \cdot {8}^{3} + \binom{5}{4} {x}^{5- 4} \cdot {8}^{4} + \binom{5}{5} {x}^{5 - 5} \cdot {8}^{5} \\ \implies(x + 8 {)}^{5} = \binom{5}{0} {x}^{5} \cdot 1 + \binom{5}{1} {x}^{4} \cdot {8} + \binom{5}{2} {x}^{3} \cdot 64+ \binom{5}{3} {x}^{2} \cdot 512 + \binom{6}{4} {x}^{1} \cdot 4096+ \binom{5}{5} {x}^{0} \cdot 32768\\ \implies(x + 8{)}^{5} = 1 \cdot {x}^{5 } \cdot 1 + 5\cdot{x}^{4} \cdot {8} + 10 \cdot {x}^{3} \cdot 64+ 10 \cdot {x}^{2} \cdot 512 + 5 \cdot{x}^{1} \cdot 4096+ 1 \cdot {x}^{0} \cdot 32768 \\ \implies \boxed{ (x + 8 {)}^{5} = {x}^{5} + 40{x}^{4} + 640{x}^{3} + 5120 {x}^{2} + 20480{x}^{}+ 32768 }[/tex]

and we're done!

Answer:

volume = x(x + 2)(x - 1)

soil = 30 ft³

Step-by-step explanation:

volume of a cuboid = width x length x height

Substituting given values into the equation:

⇒ volume = x(x + 2)(x - 1)

If width = 3ft, then x = 3:

⇒ volume = 3(3 + 2)(3 - 1)

                 = 3(5)(2)

                 = 30 ft³

Answer:

x = 8

Step-by-step explanation:

3x + 2 + 7x + 8 = 90

10x + 10 = 90

10x = 80

x = 8

The value of  [tex]\rm cot\theta = \frac{1}{ -\frac{3}{8} }[/tex]  or  [tex]\rm cot\theta = -\frac{8}{3}[/tex] the option first is correct.

It is given that the  [tex]\rm tan\theta = -\frac{3}{8}[/tex]

It is required to find which expression is equivalent to [tex]\rm cot\theta[/tex].

The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.

We have  [tex]\rm tan\theta = -\frac{3}{8}[/tex] , which is a ratio of side opposite side of an angle to the side adjacent to the angle.

We know [tex]\rm cot\theta[/tex] is a ratio of the side adjacent to the angle to the side opposite to the angle ie. it is the opposite of the [tex]\rm \tan\theta[/tex] ie.

The  [tex]\rm tan\theta = \frac{1}{cot\theta}[/tex]

or    [tex]\rm cot\theta = \frac{1}{tan\theta}[/tex]

Putting the value of [tex]\rm tan\theta[/tex] in the above equation, we get:

[tex]\rm cot\theta = \frac{1}{ -\frac{3}{8} }[/tex]  

Or

[tex]\rm cot\theta = -\frac{8}{3}[/tex]

Thus, the value of  [tex]\rm cot\theta = \frac{1}{ -\frac{3}{8} }[/tex]  or  [tex]\rm cot\theta = -\frac{8}{3}[/tex].

Know more about trigonometry here:

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Answer:

first option

Step-by-step explanation:

Answer: C. 24 units

Step-by-step explanation:

C is the correct answer. This is because the length of the segment doesn't change when reflected along the x-axis or translated left or right. The length of a segment only changes if the given figure is stretched or compressed, which doesn't occur in the given case or question.

Divide money earned by hours worked to get the hourly rate of $11.00 per gour.

Answer: C. $11.00 per hour

Answer:

16.2

Step-by-step explanation:

calculator :0

Answer:

x= -2, 0

Step-by-step explanation:

Answer:

No. Just no the formula

Hyp2= Adj2 +Opp2

The Pythagorean theorem states that the square on the hypotenuse is equal to the sum of the squares on the other two sides in a right triangle.

Pythagoras came up with a theorem that says, “the square of the hypotenuse of a right-angled triangle is equal to the sum of the square of the other two sides.” This theorem is known as the Pythagoras theorem.

Pythagorean theorem is a theorem in geometry that relates all the three sides of a right triangle.

It states that, in a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.

A right triangle is a three-sided closed geometric plane figure in which one of the 3 angles is 900.

In a right triangle, the side opposite to the right angle is the longest side and is called the hypotenuse.

The horizontal side forming the right angle is called the base of the right triangle and the vertical side is the hypotenuse.

For example, if ΔABC is a right triangle with sides AB, BC, and AC such that the triangle is right-angled at B, then the Pythagoras equation is written as:

[tex]\rm Hypotenuse ^2= Base^2+ Perpendicular^2\\\\AB^2+BC^2=AC^2[/tex]

Hence, the Pythagorean theorem states that the square on the hypotenuse is equal to the sum of the squares on the other two sides in a right triangle.

Learn more about Pythagoras' theorem here;

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Answer:

1/6.2=15/x

Step-by-step explanation:

15:x=1:6.2

Answer:

D. [tex]\frac{1}{6.2} =\frac{15}{x}[/tex]

93 meters

Step-by-step explanation:

Howard has a scale model of the Statue of Liberty

1 inch = 6.2 meters

15 inches = ? meters

[tex]\frac{1}{6.2} =\frac{15}{x}[/tex] <= cross multiply

1x = 93  <== divide both sides by 1

/1     /1

x = 93 meters <== the height of the model, our final answer

Hope this helps!

Question 1:

Removing the zero from 0.76 leads to .76 which is the same as before. Both lead to [tex]7.6 \times 10^{-1}[/tex] in scientific notation.

Personally I prefer the zero up front to make the decimal point stand out easier. Of course it's just a preference, so its up to you to decide which you prefer.

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

Question 2:

Taking the zero out of 10.25 leads to 1.25 which is definitely a different number (and smaller). Therefore, this zero is a significant digit compared to before.

is there a value to y? if not, this is what I got:

Y^2 + 2y + 3

We know, perimeter of the rectangle = 2(l +b)

where, l = length and b = breadth

Here, the perimeter of the rectangle is 48 kilometers and the height is of 10 kilometers. We can take height as the breadth.

=> Perimeter = 2(l + b)

=> 48 = 2(l + 10)

=> 48/2 = l + 10

=> l + 10 = 24

=> l = 24 - 10

=> l = 14 kilometers

Answer:

  6.2 units

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relations between trig functions and sides of a right triangle.

To find the value of x in this figure, we need to know the length of the common segment between the two triangles. That segment is opposite the 53° angle, so can be found using the sine relation:

  Sin = Opposite/Hypotenuse

  Opposite = Hypotenuse × Sin = 30·sin(53°) ≈ 23.9591

__

The side marked x is adjacent to the marked angle in that triangle, so the relevant relation is ...

  Cos = Adjacent/Hypotenuse

  Adjacent = Hypotenuse × Cos = 23.9591·cos(75°) ≈ 6.20106

The length of the side marked x is about 6.2 units.

24

Explanation:

R = D + 12 (1)

D = B + 6 (2)

R = 2*B (3)

Put (3) into (1): 2*B = D + 12 (4)

Rewrite (2) as B = D - 6 and put this into (4): 2*(D - 6) = D + 12

So: 2D - 12 = D + 12

Subtract D from both sides and add 12 to both sides to get: D = 24

(not suree)

Answer:

4units is the answer to the question

Answer:

4

Step-by-step explanation:

took the k12 test

Step-by-step explanation:

See the solution for each part

1)

2)

3)

4)

5)

Now

Answer:

[x] ≥ x

Step-by-step explanation:

Answer:

 xy

---------

x + y

Step-by-step explanation:

(xy)

-----  is in its simplest form.

(x + y)

I hope this helps!

Answer: y=x-6

Step-by-step explanation:

Step-by-step explanation:

60° + 80° + y = 180° ( being straight angle )

140° + y = 180°

y = 180° - 140°

y = 40°

Answer:

y + 6 = - [tex]\frac{1}{4}[/tex] (x + 10)

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 4x ← is in slope- intercept form

with slope m = 4

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{4}[/tex]

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = - [tex]\frac{1}{4}[/tex] and (a, b ) = (- 10, - 6 ) , then

y - (- 6) = - [tex]\frac{1}{4}[/tex] (x - (- 10) ) , that is

y + 6 = - [tex]\frac{1}{4}[/tex] (x + 10)

Answer:

17,535 dollars

Step-by-step explanation:

5% of 16,700 is 835, so add the two together and you get your answer.

Step-by-step explanation:Updated answer is the second one

Answer:

1 m/s/s.

Step-by-step explanation:

Acccelaration = rate of change of speed

= (40 - 30) /10

= 10/10

= 1 m/s/s.

Answer:

x = 35.20735

Step-by-step explanation:

Use tanФ = opposite/adjacent

tan58 = x/22

x = 35.20735

The Consecutive interior angles theorem can be used to show that the lines AB and CD are parallel

An angle is formed from the intersection of two or more lines. Types of angles are acute, obtuse, right angle.

The consecutive interior angle theorem states that if a pair of parallel line is intersected by a transversal, the pair of consecutive interior angles formed is supplementary

The Consecutive interior angles theorem can be used to show that the lines AB and CD are parallel

Find out more on angle at: https://brainly.com/question/25770607

Answer:

ans is 24000

Step-by-step explanation:

frist convert 12 into mins

/ it with 45

now multiple it with 1500

now ans 24000

(Assuming it works at a constant rate)

45 minutes = 3/4 of an hour

If it works for 12 hours, it works for 12 : 3/4 = 16 times more than 45 minutes.

Since it works at a constant rate, it must also print 16 times more paper than in 45 minutes.

So, in 12 hours, the machine print 1500 x 16 = 24000 (papers)