Unit 2 Cumulative Assessment
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Find the product of (7x - 3)(2x + 4). What is the coefficient of x when the product is written in simplest form?

Answer:

The final answer is [tex]7x +7[/tex] .

Step-by-step explanation:

-Solve equation:

[tex]5x + 7 + 2x[/tex]

-Combine like terms:

[tex]5x + 7 + 2x[/tex]

[tex]7x +7[/tex]

-Result:

[tex]7x +7[/tex]

Answer: 22 AUD x 1.2USD / 1AUD

Step-by-step explanation: The expression would be like this:   22 Australian dollars/1.2 (value of Australian dollars to US dollars) = X US dollars/1 We would get the value of x by multiplying 1 to 22 then divide it by 1.2 and we would get the US conversion from it. We could also put the expression 22=1.2x directly and we would get the US conversion from it.

Answer:

log2(0.25) = -2

512 = 8^3

Step-by-step explanation:

Rewrite the following equation in logarithmic form.   0.25 = 2^-2

Rewrite the following equation in exponential form.  log8 (512) = 3

Answer:

A) Measure of an interior angle of polygon = 150°

B) No of sides = 12

C) Sum of all interior angles = 1800°

Step-by-step explanation:

Measure of interior angle of polygon = 180°- measure of exterior angle of polygon

= 180°-30°

= 150°

B.

[tex]No.\: of \: sides = \frac{360\degree}{30\degree} = 12\\\\C.\\Sum\:of\: all \:interior\: angles \\= (n-2)\times 180\degree\\= (12-2) \times 180\degree\\= 10\times 180\degree\\= 1800\degree[/tex]

Answer:

C

Step-by-step explanation:

(x-4)(x+10)=x^2+6x-40

Answer:

C. X-4

Step-by-step explanation:

A P E X

Answer:

1 1/4 48's.

Step-by-step explanation:

5 * 12 = 60

60 / 48 = 1 12/48

= 1 1/4.

Answer:

1 48

Step-by-step explanation:

if 2 twelve is equal to 24 and 24+24= 48 then 4 12s would equal one 48 with 12 still remaining

Answer: a ≤ 4 or (-∞, 4]

Step-by-step explanation:

Here we have the inequality:

4a ≤ 16

this means that the left sides is less or equal than the right side.

First, find the equal part:

4*a = 16

a = 16/4 = 4

So the maximum possible value of a is 4.

Now, all the values of a smaller than 4 also make the inequality true (even the negative values) so the possible values of a are:

a ≤ 4 or (-∞, 4]

Answer:

Any number that is less or equal to 4 makes this inequality true.

Step-by-step explanation:

In order to calculate the numbers that make this inequality valid, we need to solve it for "a". This can be done in the same manner as we would solve an equation, although we must pay attention to the inequality. This is done below:

[tex]4*a \leq 16\\a \leq 16/4\\a \leq 4[/tex]

Any number that is less or equal to 4 makes this inequality true.

Answer:

A cone with a diameter of 18ft and a slant height of 30ft

Using Pythagorean theorem, the height is calculated by:

H = sqrt(18^2 - (30/2)^2) = 9.95

The surface area:

A = lateral surface area + base

A = pi x radius x slant height + pi x radius^2

A = pi x (30/2) x 18 + pi x (30/2)^2 = ~1555.1 (ft2)

The volume:

V = base x height x (1/3)

V = pi x radius^2 x height

V = pi x (30/2)^2 x 9.95 = 7033.2 (ft3)

Hope this helps!

:)

The trick is to exploit the difference of squares formula,

[tex]a^2-b^2=(a-b)(a+b)[/tex]

Set a = √8 and b = √6, so that a + b is the expression in the denominator. Multiply by its conjugate a - b:

[tex](\sqrt8+\sqrt6)(\sqrt8-\sqrt6)=(\sqrt8)^2-(\sqrt6)^2=8-6=2[/tex]

Whatever you do to the denominator, you have to do to the numerator too. So

[tex]\dfrac{\sqrt2+\sqrt6}{\sqrt8+\sqrt6}=\dfrac{(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)}{(\sqrt8+\sqrt6)(\sqrt8-\sqrt6)}=\dfrac{(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)}2[/tex]

Expand the numerator:

[tex](\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=\sqrt{2\cdot8}+\sqrt{6\cdot8}-\sqrt{2\cdot6}-(\sqrt6)^2[/tex]

[tex](\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=\sqrt{16}+\sqrt{48}-\sqrt{12}-6[/tex]

[tex](\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=4+\sqrt{48}-\sqrt{12}-6[/tex]

[tex](\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=-2+\sqrt{12}(\sqrt4-1)[/tex]

[tex](\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=-2+\sqrt{12}(2-1)[/tex]

[tex](\sqrt2+\sqrt6)(\sqrt8-\sqrt6}=-2-\sqrt{12}[/tex]

So we have

[tex]\dfrac{\sqrt2+\sqrt6}{\sqrt8+\sqrt6}=-\dfrac{2+\sqrt{12}}2[/tex]

But √12 = √(3•4) = 2√3, so

[tex]\dfrac{\sqrt2+\sqrt6}{\sqrt8+\sqrt6}=-\dfrac{2+2\sqrt3}2=\boxed{-1-\sqrt3}[/tex]

Answer:

We can find the radius from circumference and then area

Circumference(C) = 2πr

r = C/2π

r = 20/2π

r = 10/π

Area = πr²

Area = π × 10/π × 10/π

Area = 100/π

Area = 100/3.14

Area = 10000/314 = 31.84 cm² (approx)

Area = 32 cm² (Rounding to nearest whole number)

Answer:

32 m²

Step-by-step explanation:

We need to work out the area of the flower garden when we are given the circumference. First we need to know the formula's for area of circle and circumference of circle which are

→ Area of a circle = π × r² where 'r' is the radius

→ Circumference of a circle = 2 × π × r where 'r' is the radius

So we need to form an equation with the circumference of a circle formula and work out the radius in order to find the area so,

In an equation our aim is to find the value of what we are looking for as well as keeping the equation balanced. For example if we divided by 2  only from one side then the equation would change so it's an important rule to keep in mind when solving equations, that you need to keep both sides of the equation the same.

2 × π × r = 20

→ Substitute 3.14 for π

2 × 3.14 × r = 20

→ Simplify

6.28 × r = 20

→ Divide both sides by 6.28 to isolate 'r'

r = 3.18471338

So now we now the radius of the circle we can substitute the radius into the area of circle formula

Area = π × r²

→ Substitute 3.14 for π and r for 3.18471338

Area = 3.14 × 3.18471338²

Area = 31.847133842

To the nearest whole number your answer is 32 m²

Answer:a

Step-by-step explanation:

Answer:

It is A, y = 9,958(0.972)x

Step-by-step explanation:

Answer:

b=10, a=13

Step-by-step explanation:

let s number of yellow = a

number of blue = b

we have

a+b =23

2b - a = 7

->a+b +2b -a = 23+7

-> 3b = 30

->b = 10

->a = 13

Answer:

b=9

Step-by-step explanation:

move the 4b over to the other side by adding it to both sides

[tex]-3b(+4b)=9-4b(+4b)[/tex]

[tex]1b=9[/tex]

The answer is B part

As the requirement for the student is either a senior or one who studies maths or both.

So, just add the values within the two venn circles divide it by total no of values.

=> 240+40+110/240+40+110+840

=> 360/1200

Answer:

B

Step-by-step explanation:

840 people aren't senior or don't takes math.

210 + 40 = 250 are seniors

110 + 40 = 150 people take math

In this class has 840 + 210 + 40 + 110 = 1200 people => All

210 + 40 + 110 = 360 people are seniors or take math. => P( S U M)

Probabilty that a randomly selected student is a senior or takes math =>[tex]\frac{P(S U M)}{All}[/tex]

[tex]\frac{P(S U M)}{All} = \frac{360}{1200}[/tex]

Hope this helps ^-^

Answer:

sin^2(45) = (√2/2)^2 = 1/2

Step-by-step explanation:

sin2x = sin2 * x = 0.909x

sin(2(45)) = sin90 = 1

Hope this helps.

Answer:

The answer to this is [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

I did the assignment, hope it helps! :)

Answer: 7 1/30

Step-by-step explanation:

Tina loves to read. Before breakfast, she read 2 1/2 pages, at lunch she read 3 1/5 pages, and after dinner she read 1 1/3 pages. To find the total, we add all the pages together. This will be:

2 1/2 + 3 1/5 + 1 1/3

The LCM of 2, 5 and 3 is 30.

= 2 15/30 + 3 6/30 + 1 10/30

= 6 31/30

= 7 1/30.

Answer:

7,1 × 10-⁶

Step-by-step explanation:

Once you move the comma 1 time by right (,) you have -1, so by moving it six times, you have 7,1 × 10-⁶

Answer:

To do this you need to fill in the equation:  1/2 height*sidelength *width. So, height = 8 ft, side length = 4 ft, and width = 24 ft. So, plugging in the numbers you get:

1/2(8) * 4 * 24 =

4*4*24 = 384 ft

Step-by-step explanation:

Answer:

345 ft^3

Step-by-step explanation:

B=1/2(5)(6)=15

V=15(23)=345

Answer:

Step-by-step explanation:

For example, if your money earns an 8 percent interest rate, it will triple in 14 years and 5 months (115 divided by 8 equals 14.4). If your money earns a 5 percent interest rate, it will triple in 23 years (115 divided by 5 equals 23).

Only one of those is actually a prime factorization.  Demand better from your teacher.  Anyway, I think they're just asking us to take out the calculator and enter the multiplication into it.

5) 22 isn't prime, neither is 52.  Answer:  3432

6) 32 isn't prime.  Answer: 448

7) 33 isn't prime.  Answer: 165

8)  Finally a real prime factorization.  Answer: 106

Answer:

P(B) = 0.85

Step-by-step explanation:

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

[tex]P(A) = 0.24, P(B|A) = 0.85[/tex]

These events are independent.

This means that [tex]P(A \cap B) = P(A)*P(B)[/tex]. So

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

[tex]P(B|A) = \frac{P(A)*P(B)}{P(A)}[/tex]

[tex]P(B|A) = P(B)[/tex]

So

[tex]P(B) = 0.85[/tex]

Answer:

the anser is 24,32,56

Step-by-step explanation:

i did it got it wrong and then it gave me the right anser witch is that

Answer:

24,32,and 56 is right. trust me

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given

Solving for z:

Answer:

3540

Step-by-step explanation:

There are 3520 yards in two miles and 1760 in one mile you multiply 1760 by 2 then add 20

option b is the correct answer

Answer:

Step-by-step explanation:

Multiplicity of a number is the number of times the factor of a given function appears in the factor form of such given equation. For us to know the multiplicity of the root of the function, first we must know its root.

Factorizing the given quadratic function  x²−8x+16=0

[tex]x^{2} -4x-4x+16 = 0\\x(x-4)-4(x-4)=0\\(x-4)(x-4) = 0\\x-4 = 0 and x-4 = 0\\x = 4\ twice[/tex]

Since the root of the function which is 4 appears twice then the multiplicity of the root is 2

Answer:

work is shown and pictured

Answer:

6 + 6x

Step-by-step explanation:

9 - (3-6x) = 9 - 3 - (-6x)

= (9-3) +6x

= 6 + 6x

1) expand the bracket

2) group like terms together

3) simplify to form expression

Answer:

The probability is 1/36.

Step-by-step explanation:

2/3 are dog owners

1/6 are cat owners

1/6 are bird owners

If you choose two owners, there is a 1/6 chance that you will choose a cat owner and a 1/6 chance you will choose a bird owner. Each of these are independent, so you simply multiply 1/6 by 1/6.

1/6 * 1/6= 1/36

Answer:

For online calculators you can type sqrt() or just sqrt and it will do it for you

Answer:

Step-by-step explanation:

To simplify radicals that are not perfect squares, we need a new method.

Example: [tex]\sqrt{27}[/tex]

27 is not a perfect square square the square root cannot be used.

[tex]\sqrt{27} = 5.19615242271[/tex]

To solve this, we need to break down the radical into simpler parts.

[tex]\sqrt{27} = \sqrt{3} * \sqrt{9}[/tex]

[tex]\sqrt{9} = 3[/tex]

[tex]\sqrt{3}[/tex] cannot be simplified

[tex]\sqrt{27}[/tex] = 3[tex]\sqrt{3}[/tex]

Good luck on your test!

I'm always happy to help :)