Which statement is true? Question 6 options: A) |–3| = 3 and –|–4| = –4 B) –|3| = 3 and |4| = 4 C) |–3| = 3 and –|4| = 4 D) |–3| = 3 and |–4| = –4

Answer:

26) Let the first number be x.

Sum of three consecutive even numbers:

[tex]x+(x+2)+(x+4)=-84[/tex]

[tex]x+x+2+x+4=-84\\[/tex]

[tex]3x+6=-84[/tex]

Subtract 6 from both sides:

[tex]3x+6-6=-84-6[/tex]

[tex]3x=-90[/tex]

Divide both sides by 3:

[tex]\frac{3x}{3}=\frac{-90}{3}[/tex]

[tex]x=-30[/tex]

To find the other two numbers, add 2 and 4 respectively:

[tex](-30+2=-28)(-30+4=-26)[/tex]

27) Let the first number be x.

Sum of three consecutive odd integers:

[tex]x+(x+2)+(x+4)=141[/tex]

[tex]3x+6=141[/tex]

Subtract 6 from both sides:

[tex]3x+6-6=141-6\\3x=135[/tex]

Divide both sides by 3:

[tex]\frac{3x}{3}=\frac{135}{3}\\x=45[/tex]

To find the other two numbers, add 2 and 4 respectively:

[tex](45+2=47)(45+4=49)[/tex]

28) Let the first number be x.

Sum of four consecutive integers:

[tex]x+(x+1)+(x+2)+(x+3)=54[/tex]

[tex]4x+6=54[/tex]

Subtract 6 from both sides:

[tex]4x+6-6=54-6\\4x=48[/tex]

Divide both sides by 4:

[tex]\frac{4x}{4}=\frac{48}{4}\\x=12[/tex]

To find the other three numbers, add 1, 2 and 3 respectively:

[tex](12+1=13)(12+2=14)(12+3=15)[/tex]

29) Let the first number be x.

Sum of four consecutive integers:

[tex]x+(x+1)+(x+2)+(x+3)=-142[/tex]

[tex]4x+6=-142\\[/tex]

Subtract 6 from both sides:

[tex]4x+6-6=-142-6[/tex]

[tex]4x=-148[/tex]

Divide both sides by 4:

[tex]\frac{4x}{4}=\frac{-148}{4}\\x=-37[/tex]

To find the other three numbers, add 1, 2 and 3 respectively:

[tex](-37+1=-36)(-37+2=-35)(-37+3=-34)[/tex]

Answer:

35 meters / minute.

Step-by-step explanation:

Speed of the leaf = 140 / 4 = 35 meters / minute.

Answer:

h(t) = 100(1.02)t + 20t + 10

Step-by-step explanation:

I got it right on the test : )

Answer:

h (t) = 100(1.02)t + 20t + 100

Step-by-step explanation: edge 2021

took the unit test got it right.

16 avocados costs = $8, 20 avocados costs = $10 and 9 avocados costs = $4.5

The amount of money that a company spends on the creation or production of goods or services.

Given that, Eight avocados cost $4.

Therefore, each of them costs = 4/8 = 1/2

So, 16 avocados = 16*1/2 =$8

20 avocados = 20*1/2 =$10

9 avocados = 9*1/2 =$4.5

Hence, 16 avocados costs = $8, 20 avocados costs = $10 and 9 avocados costs = $4.5

For more references on Cost, click;

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Answer:

3:4

Step-by-step explanation:

Answer: Four hundred and thirty two point nine - eight.

Step-by-step explanation:

Hey there! I'm happy to help!

With the numbers before the decimal, you just say it normally. After the decimal, you just name the digits.

So, you would call this number four hundred thirty-two point nine eight.

Have a wonderful day! :D

Answer:

-8 + i

Step-by-step explanation:

(-3 + 2i) * (2 + i)

= -6 + -3i + 4i + 2i^2

= -6 + i - 2

= -8 + i

Answer:

[tex]8x+9<4[/tex] and [tex]8x+9>-4[/tex].

Step-by-step explanation:

The given inequality is

[tex]|8x+9|<4[/tex]

We need to rewrite the given inequality as two linear inequalities.

We know that |8x+9|>0 but (8x+9) can be positive or negative.

For [tex]|8x+9|<4[/tex],  the value of (8x+9) must be lies between -4 and 4.

i.e., [tex]-4<8x+9<4[/tex]

If 8x+9 positive, then

[tex]8x+9<4[/tex]      ...(1)

If 8x+9 negative, then

[tex]8x+9>-4[/tex]      ...(2)

Therefore, the two inequalities are [tex]8x+9<4[/tex] and [tex]8x+9>-4[/tex].

Answer:

Jacinta will have more money

Step-by-step explanation:

The interest amount is provided below for quarterly and daily compound:

Jacinta will have more money

Step-by-step explanation:

55. 162 +54=216

216-75=141

balance $141

Answer:

  k = 5

Step-by-step explanation:

The value of k is added to each y-coordinate, so represents the amount of up-shift. If the shift up is 5 units, then k=5.

Answer:

k = 5

Step-by-step explanation:

I got it right on the quiz

Answer: First step would be doing the () first. The third step would be 4 times 0. I think so, forgive me if I’m wrong.

Step-by-step explanation:

Answer:

5.5

Step-by-step explanation:

divide the length value by 12

Answer:

5.5 ft

Step-by-step explanation:

30cm=1ft

12inch= 1ft

66/12 = 5.5ft

Answer:

[tex]\displaystyle \frac{\cos x}{1 + \sin x} = \tan\left(\frac{\pi}{4} - \frac{x}{2}\right)[/tex].

Overview of the steps:

Step-by-step explanation:

Double-angle identity of sines and cosines:

Pythagorean identity for the sine and cosine of the same angle:

[tex]1 = \cos^2\alpha + \sin^2\alpha[/tex].

Angle sum and difference identity of sines and cosines:

[tex]\sin(\alpha - \beta) = \sin\alpha\, \cos\beta - \cos\alpha \, \sin\beta[/tex].

[tex]\cos(\alpha - \beta) = \cos\alpha\, \cos\beta + \sin\alpha \, \sin\beta[/tex].

Consider [tex]x[/tex] as the sum of two angles of size [tex](x/2)[/tex]. Start by applying the double-angle identity to the left-hand side.

[tex]\begin{aligned} \text{L.H.S.}&= \frac{\cos(x)}{1 + \sin(x)} \\ &= \frac{\cos^2(x / 2) - \sin^2(x / 2)}{1 + 2\, \sin(x / 2)\, \cos(x / 2)}\end{aligned}[/tex].

Apply the Pythagorean identity to rewrite the "1" in the denominator as [tex]\left(\cos^2(x / 2) + \sin^2(x / 2)\right)[/tex].

[tex]\begin{aligned} \text{L.H.S.}&= \frac{\cos(x)}{1 + \sin(x)} \\ &= \frac{\cos^2(x / 2) - \sin^2(x / 2)}{1 + 2\, \sin(x / 2)\, \cos(x / 2)}\\ &= \frac{\cos^2(x / 2) - \sin^2(x / 2)}{\sin^2(x/2) + 2\,\sin(x/2)\, \cos(x/2) + \cos^2 (x/2)}\end{aligned}[/tex].

Note that the denominator is now a perfect square. On the other hand, the numerator is in the form [tex](x^2 - y^2)[/tex], which is equal to [tex](x + y)\, (x - y)[/tex]. Rewrite and simplify this expression:

[tex]\begin{aligned} \text{L.H.S.}&= \frac{\cos(x)}{1 + \sin(x)} \\ &= \frac{\cos^2(x / 2) - \sin^2(x / 2)}{1 + 2\, \sin(x / 2)\, \cos(x / 2)}\\ &= \frac{\cos^2(x / 2) - \sin^2(x / 2)}{\sin^2(x/2) + 2\,\sin(x/2)\, \cos(x/2) + \cos^2 (x/2)} \\[1em] &= \frac{(\cos(x/2) + \sin(x/2))\, (\cos(x/2) - \sin(x/2))}{\left(\sin(x/2) + \cos(x/2)\right)^2} \\ &= \frac{\cos(x/2) - \sin(x/2)}{\sin(x/2) + \cos(x/2)}\end{aligned}[/tex].

The tangent of an angle is equal to the ratio between its sine and its cosine. Apply the angle sum and difference identity of sine and cosine to the right-hand side.

Note, that the sine and cosine of [tex](\pi/4)[/tex] are both equal to [tex]\left(\sqrt{2}/2\right)[/tex].

[tex]\begin{aligned}\text{R.H.S.} &= \tan\left(\frac{\pi}{4} - \frac{x}{2}\right) \\ &= \frac{\sin((\pi/4) - (x/2))}{\cos((\pi/4) - (x/2))}\\ &= \frac{\left(\sqrt{2}/2\right)\, \cos(x/2) - \left(\sqrt{2}/2\right)\, \sin(x/2)}{\left(\sqrt{2}/2\right)\, \cos(x/2) + \left(\sqrt{2}/2\right)\, \sin(x/2)} \\ &= \frac{\cos(x/2) - \sin(x/2)}{\cos(x/2) + \sin(x/2)}\end{aligned}[/tex].

Therefore:

[tex]\displaystyle \text{L.H.S.} = \frac{\cos(x/2) - \sin(x/2)}{\sin(x/2) + \cos(x/2)} =\text{R.H.S.}[/tex].

[tex]\displaystyle \frac{\cos x}{1 + \sin x} = \tan\left(\frac{\pi}{4} - \frac{x}{2}\right)[/tex].

Answer:

S = { (4), (5), (1,4), (1,5), (2,4), (2,5), (3,4), (3,5), (1,2,3,4), (1,2,3,5), (2,1,3,4) (2,1,3,5), (3,1,2,4), (3,1,2,5) }

A ={(4), (5)}

Step-by-step explanation:

Given that:

Among the three copies, (1,2,3) are the first printings, and (4,5) are the second printings.

A student who examines these books in random order stops when a second printing has been selected.

Thus, we can compute the sample space associated with these experiments as:

S = { (4), (5), (1,4), (1,5), (2,4), (2,5), (3,4), (3,5), (1,2,3,4), (1,2,3,5), (2,1,3,4) (2,1,3,5), (3,1,2,4), (3,1,2,5) }

Suppose A represents the event that we must examine exactly one book.

Then the outcomes of A are:

A ={(4), (5)}

Answer:g(x)=-4^2+4x-5

Step-by-step explanation:

Answer:

D. 3

Step-by-step explanation:

We can see from the graph that there are 3 lines. All 3 lines look linear, and if a line is linear, x and y are proportional. Therefore, if all 3 lines are linear, then we have 3 proportional relationships.

Answer:

  13.25 ft

Step-by-step explanation:

Let w represent the width of the window. Then w-5 represents the length, and the perimeter is ...

  P = 2(L+W)

  43 = 2((w-5) +w) = 4w -10

  53/4 = w = 13.25 . . . feet

The width of the window is 13.25 ft.

Answer:

[tex]\huge\boxed{\sf f = -4}[/tex]

Step-by-step explanation:

[tex]\sf -5f = 20\\\\Dividing\ both\ sides\ by\ -5\\\\\frac{-5f}{-5} = \frac{20}{-5} \\\\f = -4[/tex]

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

M= D x V, V= M x D

Step-by-step explanation:

You just do the opposite of division since the original is:

Density= Mass/ Volume

Answer:

  4 < 2a -4 < 10

Step-by-step explanation:

You have an expression for 'a'. To get an expression for 2a-4, multiply it by 2 and subtract 4.

  4 < a < 7

  8 < 2a < 14 . . . . . . multiply by 2

  4 < 2a -4 < 10 . . .  subtract 4

Solution:

3[(8 - 4)^5] ÷ 8

3[4^5] ÷ 8

3[1024] ÷ 8

3072 ÷ 8

384

Best of Luck!

Answer:

384

Step-by-step explanation:

[tex]3[(8-4)^5][/tex]÷[tex]8[/tex]

Using the rules of PEMDAS I know that I have to do the math inside of the parenthesis first.

 8 - 4 = 4

Our new equation is

[tex]3[(4)^5][/tex]÷[tex]8[/tex]

Next we have to solve for the exponent.

[tex]4^5[/tex]  = [tex]4*4*4*4*4[/tex] = 1,204

Our new equation looks like:

[tex]3[1024][/tex]÷[tex]8[/tex]

Now we will multiply, because we follow the rules of operation.

[tex]3 *1024= 3072[/tex]

Finally we will divide 3,072 by 8.

[tex]3072/8= 384[/tex]

Our final answer is:

384

Answer:

200000+800000+0+2000+100+30+6

Step-by-step explanation:

2,000,000

800,000

0

2,000

100

30

+ 6

_________

Answer:

What do u mean? For example, meters (works with other units of measurement) its based on an Acronym. King Henry Died By Drinking Chocolate Milk. The first letters stand for: Kilo, Hecto, Deca, Base (your unit of measurement), Deci, Centi, Mili

Step-by-step explanation:

Answer:

0.20613038098

Step-by-step explanation:

The formula for Binomial Probability =

P(X) =[ n!/(n - x)! × x! ] × p^x × q^n - x

From the question

x = 5

n = 15

p = 0.3

q = 1 - p

= 1 - 0.3 = 0.7

P(x = 5) = [15!/(15 - 5)! × 5! ] × 0.3^5 × 0.7^15 - 5

P(x = 5) = 3,003 × 0.3^5 × 0.7^10

P(x = 5) = 0.20613038098

Therefore, P(x = 5) = 0.20613038098

Answer: D

Step-by-step explanation:

i just had this question on a quiz and it said the correct answer was /89

Answer:

g = 15/7

Step-by-step explanation:

3g - 9 + 11g - 21

group like terms

3g + 11g = 21 + 9

14g = 30

g = 30/14

g = 15/7