the object on the right is made from a square-based pyramid joined to a cuboid.
the base of the cuboid and the base of the pyramid are both squares of side 6cm.
the bright of the cuboid is 9cm and the total height of the object is 17cm.
the total mass of the object is 970g.
the cuboid is made from wood with density 0.68g/cm^3
the pyramid is made from steel.
calculate the density of the steel in g/cm^3.
you must show your working.

Answer:

Equation of a line is y = mx + c

where m = slope and c = y intercept

Using point ( -2 , 4) and m = 2

Equation of the line is

y - 4 = 2(x + 2)

y - 4 = 2x + 4

y = 2x + 4 + 4

y = 2x + 8

Hope this helps.

Equation of a line passing through (-2, 4) and slope '2' will be,

y = 2x + 8

Given in the question,

Equation of a line passing through a point (h, k) and slope 'm' is given by the equation,

y - k = m(x - h)

Substitute the values in the given equation,

y - 4 = 2[x - (-2)]

y - 4 = 2(x + 2)

y = 2x + 4 + 4

y = 2x + 8

       Therefore, equation of the line passing through (=2, 4) and slope '2' will be y = 2x + 8

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Answer: 65 grams

Step-by-step explanation:

If 130 grams of a gold alloy (a mixture of gold and one or more other metals) containing 85% pure gold, that means the percentage of other metals will be;

100 - 85 = 15 %

You should first calculate the amount of gold that makes up this percentage.

That is, 85% of 130 grams.

85/100 × 130 = 110.5

Then, let X be what will be added to the above value to make 90%. So,

(110.5 + X) / ( 130 + X ) × 100 = 90

Divide both sides by 100

(110.5 + X) / ( 130 + X ) = 90/100

(110.5 + X) / ( 130 + X ) = 0.9

Cross multiply and open the bracket

110.5 + X = 117 + 0.9X

Collect the like terms

X - 0.9X = 117 - 110.5

0.1X = 6.5

Divide both sides by 0.1

X = 6.5/0.1

X = 65 grams

Therefore, the amount of pure gold that should be added is 65 grams

Answer:

√40 ≈ 6.32

√75 ≈ 8.66

√90 ≈ 9.49

√245 ≈ 15.65

√450 ≈ 21.21

√640 ≈ 25.30

√675 ≈ 25.98

Step-by-step explanation:

You can use your calc or estimate your answer by simplifying (like √640 is 8√10, and estimate the square root of 10). However, getting decimals will require you to use a calc.

Answer:

do we have opitions

Step-by-step explanation:

The result of dividing (3x³ + 2x² + 10) by (x - 3) is 3x² + 11x + 33 with a remainder of 109.

dividing (3x³ + 2x² + 10) by (x - 3) using long division

               3x² + 11x + 33

              _______________________

x - 3  |   3x³ + 2x² + 0x + 10

              -(3x³ - 9x²)

            _______________________

                      11x² + 0x + 10

                      -(11x² - 33x)

                   _______________________

                               33x + 10

                               -(33x - 99)

                            _______________________

                                         109

The result of dividing (3x³ + 2x² + 10) by (x - 3) is 3x² + 11x + 33 with a remainder of 109.

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Answer:

x > -3

Step-by-step explanation:

-3x - 3 < 6

Add 3 to each side

-3x - 3+3 < 6+3

-3x < 9

Divide by -3 remembering to flip the inequality

-3x/-3 > 9/-3

x > -3

Answer:

The amount of energy it takes to lift a box might be a function of the weight of the objects inside the box. Work is proportional to force and distance. The force of the box is the weight itself of the box. Hence the answer to this problem is B.

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]Hypotenuse = 8\\Adjacent = x\\ Angle = \alpha = 43\\\\Using ; SOHCAHTOA , \\Cos \alpha = \frac{adj}{hyp} \\Cos 43 =\frac{x}{8} \\0.73= \frac{x}{8} \\x = 0.73*8\\x = 5.84\\x = 5.8[/tex]

I hope i am correct

Answer:

Step-by-step explanation:

angle pair for vertical angles is called straight angle....

the joining between two pages of a book is a vertical angle....

the road itself is a vertical angle

Answer:

The probability distribution of x is given by

P(x) = ⁿCₓ pˣ (1 - p)ⁿ⁻ˣ

Where n is the number of trials, x is the variable of interest and p is the probability of success.

P(x = 0) = 0.49

P(x = 1) = 0.42

P(x = 2) = 0.09

Step-by-step explanation:

The binomial distribution has the following features:

• There are n repeated trials and are independent of each other.

• There are only two possibilities: US adults attend  church every Sunday or US adults do not attend  church every Sunday

• The probability of success does not change with trial to trial.

Let x represent the  number in this sample who attend church every

Sunday, the probability distribution of x is given by

P(x) = ⁿCₓ pˣ (1 - p)ⁿ⁻ˣ

Where n is the number of trials, x is the variable of interest and p is the probability of success.

For the given case

Probability of success = p = 0.30

Number of trials = n = 2

Variable of interest = x = 0, 1, 2

For P(x = 0):

Here we have x = 0, n = 2 and p = 0.30

P(x = 0) = ²C₀(0.30⁰)(1 - 0.30)²⁻⁰

P(x = 0) = 0.49

For P(x = 1):

Here we have x = 1, n = 2 and p = 0.30

P(x = 1) = ²C₁(0.30¹)(1 - 0.30)²⁻¹

P(x = 1) = 0.42

For P(x = 2):

Here we have x = 2, n = 2 and p = 0.30

P(x = 2) = ²C₂(0.30²)(1 - 0.30)²⁻²

P(x = 2) = 0.09

Answer:

might be 20.8 lmk

Step-by-step explanation:

Answer:

x = 12√3

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

[tex]6(3+4)-5(1+2)= \\\\6(7)-5(3)= \\\\42-15= \\\\27[/tex]

Hope this helps!

Answer:

27

Step-by-step explanation:

6(3+4)-5(1+2)=

6(7)-5(3)=

42-15=

27

Answer:

$400

Step-by-step explanation:

Seeing as VAT adds to the original price we needed to go DOWN in value to find the original price. So all I did was go through trial and error and I went and saw what 20% of number like 450 and 420 were and then I added them to the price to see if it would get to £480. So when I checked 20 percent of 400 I got 80 which added to 400 gives the market price of £480.

Answer:

12

Step-by-step explanation:

The area of a rectangle is l × w.

x × 11/3 = 44

x = 44 × 3/11

x = 12

Answer:

39 books

Step-by-step explanation:

Solve the equation in order of PEMDAS (parentheses, exponents, multiplication, division, addition, subtraction)

2(16) + 7

Multiply 2(16) first.

2(16) = 32

Then add 7.

32 + 7 = 39

Answer:

C -3/5

Step-by-step explanation:

3 / -5

It doesn't matter where the negative sign goes

-3/5 or

-  3/5

We have one negative sign

Answer:

C. -3/5

Step-by-step explanation:

Answer:

W=2.615

Step-by-step explanation:

9w-36-7w=15w-2

2w-36=15w-2

15w-2w=-36+2

13w=34

w=34/13

W=2.615

Answer:

Brailniest

Step-by-step explanation:

0.25k+1.5-k-3.5

-0.75k-2

so you are right

Answer:

It is right

Step-by-step explanation:

0.25k - k = -0.75k

1.5 - 3.5 = 2

Answer:false

Step-by-step explanation:

(-7)^2

(-7)*(-7)

49

49 is a positive number

Answer:

It is false

Step-by-step explanation:

It is false because if you have two groups of negatives, it is positive. (-7)^2 is the same as -7x-7. Two negatives equal a positive, so the answer should be 49. 49 is positive so it is false.

Answer:

B). Graph B

Step-by-step explanation:

A Histogram is a graphic representation of data using bars varying in height as per the range of values.

In the given question, the second option correctly represents the data provided in the table using a histogram. It portrays the class ranging from 0.320 - 0.329 with an average of 1 in the first bar, from 0.330 - 0.339 with an average of 14 runs in the second bar, and moves so on till 0.360-0.369 correctly. The other options fail to portray the numerical distribution appropriately and hence, option B is the correct answer.

Hey there! :)

Answer:

The 2nd choice.

Step-by-step explanation:

Begin by solving the inequality |g + 2| > 3. There is a negative and positive solution:

g + 2 > 3

g > 1

-(g + 2) > 3

-g - 2 > 3

-g > 5

g < -5

Therefore, the number-line showing solutions LESS THAN -5 and GREATER THAN 1 is the 2nd choice.

**Remember, for '<' and '>' signs without the EQUAL TO, the points are open circles.

Answer:

B)

Step-by-step explanation:

correct on edge test ✅

Answer:

third option

Step-by-step explanation:

Given

x² - x - 6 = 0 ← in standard form

(x - 3)(x + 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x + 2 = 0 ⇒ x = - 2

Answer:

x = -2 or x = 3

Step-by-step explanation:

The answer to your question is C.

Answer: Number of Cavities

Answer:

B. -2

Step-by-step explanation:

If you distribute the -2, you can see that you have -2x. Your slope-intercept form y = mx + b tells you that mx is always your slope. Therefore, your answer is B.

Answer:

Step-by-step explanation:

Answer:

I hope this helps.

Step-by-step explanation:

Answer:

It is either 1 or 0.9

Step-by-step explanation:

COS=. adjacent / hypotenuse

adjacent   =  x

hypotenuse =19

COS= x / 19

cross multiply

x = COS (9)

x=0.91113026

The length of shorter side is 9.5 cm.

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

Ratio = 1 : 2 : 3

Hypotenuse = 19 cm

The sides are x, 2x and 3x.

x+ 2x + 3x = 180

6x= 180

x= 30 degree

and, 3x= 90 degree

Now, using Trigonometry

sin 30 = y/ 19

y= 19/2

y= 9.5

Hence, the length of shorter side is 9.5 cm

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Answer:

£25

Step-by-step explanation:

Total price- £53.55

Pair of trainers cost- £38 before discount

Discount= 15%

Cost of pair of trainers after discount:

Price of the watch after discount:

Price of the watch before discount:

Answer:

Answer Choice 'A' would be correct.

Answer:

Solution,

Hypotenuse(h)=X

Perpendicular (p)=9

Base(b)=12

Now,

Using Pythagoras theorem,

[tex] {h}^{2} = {p}^{2} + {b}^{2} \\ or \: {x}^{2} = {(9)}^{2} + {(12)}^{2} \\ or \: {x}^{2} = 81 + 144 \\ or \: {x}^{2} = 225 \\ or \: x = \sqrt{225} \\ or \: x = \sqrt{ {(15)}^{2} } \\ x = 15[/tex]

hope this helps...

Good luck on your assignment...

The length of the hypotenuse in the given triangle is A. 15 units.

This type of question makes a right-angled triangle that can be solved by Pythagoras's theorem.

In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.

Given, the base of the triangle is 12 units and the height is 9 units.

∴ x² = 9² + 12².

x² = 144 + 81.

x² = 225.

x = + 15 units.

So, the length of the hypotenuse is 15 units.

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