Seven times the sum of 4 and some number is 42

Here are the expressions on the left matched with the simplifed form on the right:

Here are some mathematical rules:

Also, this sign | | indicates that the number is postive.

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Answer:

modulus of  |9+40i|  is 41

Step-by-step explanation:

Let z = 9+40i

then

|z| = [tex]\sqrt{9^{2}+40^{2} }[/tex]

   = [tex]\sqrt{81+1600}[/tex]

   = [tex]\sqrt{1681}[/tex]

   = 41

|z| = 41

Answer:

Step-by-step explanation:

1. |9+40i| = 41

2. |-10+24i| = 26

Answer:

200 is the maximum amount

Step-by-step explanation:

94x100=9400

9400/47=200

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Answer:

C. (-1,-2)

Step-by-step explanation:

Since C internally divides AB in the ratio AC/CB = 1/2 = m/n where m = 1 and n = 2, we use the formula for internal division.

Let A = (x₁, y₁) = (5, 16), B = (x₂, y₂) and C = (x, y) = (3, 10)

So x = (mx₂ + nx₁)/(m + n)

y = (my₂ + ny₁)/(m + n)

Substituting the values of the coordinates, we have

x = (mx₂ + nx₁)/(m + n)

3 = (1 × x₂ + 2 × 5)/(2 + 1)

3 = (x₂ + 10)/3

multiplying through by 3, we have

9 = x₂ + 10

x₂ = 9 - 10

x₂ = -1

y = (my₂ + ny₁)/(m + n)

10 = (1 × y₂ + 2 × 16)/(2 + 1)

10 = (x₂ + 32)/3

multiplying through by 3, we have

30 = y₂ + 32

y₂ = 30 - 32

y₂ = -2

So, the coordinates of B are (-1, -2)

Answer:

5u - 23

Step-by-step explanation:

Answer:

4( 2u - 2) - 3(u + 5)​

(4*2u + 4*-2)-(3*u + 3*5)

8u-8-3u+15

8u-3u-8+15

5u+7

Step-by-step explanation:

I hope this helped you.

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If there are 3 cups of strawberries per 6 liters of smoothie, that means that there is [tex]\frac{1}{2}[/tex] cups of strawberries per liter of smoothie.

[tex]\frac{3}{6}=\frac{1}{2}[/tex]

Hope this helps.

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Step-by-step explanation:

A straight line graph is of the form:

y = mx+b

So we get our equation in this form:

9=2x+3y

or, 9-2x=3y

or, -2x+9 = 3y

or, y= (-2x+9)/3

or, y = -2/3x + 3

So,

Slope(m)=−2/3

y-intercept (b) = 3

Therefore, slope(m) is -2/3x and y-intercept(b) is 3.

Answer:

28 (0,2,4,14,28)

34 (0,2,17,34)

42 (0,2,6,7,21,42)

the greatest common factor is 2 because it's the greatest number that can be divided by 28, 34 and 42

Answer:

31536000

Step-by-step explanation:

365 days x 24 hours x 60 minutes x 60 seconds = 31536000

Step-by-step explanation:

N(t) is continuous at t = 6, so f(6) = 25(6) + 150 = 300.

f(0) = 80.

f(t) is continuous, so by Intermediate Value Theorem, f(t) must equal 250 at some point between t=0 and t=6.

Answer:

C

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

2/3=66 therefore it also equals 2/3%

Answer: C

Step-by-step explanation:

First find the decimal of 2/3  

Divide it  2/3 = 0.6666666

Now multiply it by 100 to convert it to a percent  

You get 66.66..%  which is the same as 66 2/3%

Answer:

Exact form: [tex]9 \frac{41}{51}[/tex]

Decimal form: [tex]9.80392156[/tex]

Step-by-step explanation:

[tex]41\frac{2}{3}[/tex] ÷ [tex]4\frac{1}{4}[/tex]

Let's put everything into a fraction.

[tex]\frac{41\frac{2}{3} }{4\frac{1}{4} }[/tex]

Now we have an answer.

Exact form: [tex]9\frac{41}{51}[/tex]

Decimal form: [tex]9.80392156[/tex]

Hope this helps!

Answer:

1.618

The Fibonacci sequence is significant because of the so-called golden ratio of 1.618, or its inverse 0.618. In the Fibonacci sequence, any given number is approximately 1.618 times the preceding number, ignoring the first few numbers.

Step-by-step explanation:

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[tex]\Large \boxed{\sf golden \ ratio}[/tex]

A series of integers known as the Fibonacci sequence begins with a zero, is followed by a one, another one, and then a series of increasing numbers. Each number in the series equals the sum of the two numbers before it. Every succeeding pair of Fibonacci numbers has a quotient resembling the golden ratio.

Question:

Express each vector as a product of its length and direction.

[tex]\frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k[/tex]

Answer:

[tex]\frac{1}{\sqrt{2}}[/tex] [tex](\frac{1}{\sqrt{3}}i - \frac{1}{\sqrt{3}}j - \frac{1}{\sqrt{3}}k)[/tex]

Step-by-step explanation:

A vector v can be expressed as a product of its length and direction as follows;

v = |v| u

Where;

|v| = length/magnitude of v

u = unit vector in the direction of v

---------------------------------------------------------------------------------------

Let the given vector be v, i.e

[tex]v = \frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k[/tex]

(i) The length/magnitude |v| of vector v is therefore,

|v| = [tex]\sqrt{(\frac{1}{\sqrt{6}})^2 + (-\frac{1}{\sqrt{6}})^2 + (-\frac{1}{\sqrt{6}})^2[/tex]

|v| = [tex]\sqrt{(\frac{1}{6}) + (\frac{1}{6}) + (\frac{1}{6})[/tex]

|v| = [tex]\sqrt{(\frac{3}{6})[/tex]

|v| = [tex]\sqrt{(\frac{1}{2})[/tex]

|v| = [tex]\frac{1}{\sqrt{2}}[/tex]

(ii) The unit vector u in the direction of vector v, is therefore,

u = [tex]\frac{v}{|v|}[/tex]

[tex]u = \frac{\frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k}{\frac{1}{\sqrt{2}}}[/tex]

[tex]u = \sqrt{2}(\frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k)[/tex]

[tex]u = (\frac{\sqrt{2}}{\sqrt{6}}i - \frac{\sqrt{2}}{\sqrt{6}}j - \frac{\sqrt{2}}{\sqrt{6}}k)[/tex]

[tex]u = (\frac{1}{\sqrt{3}}i - \frac{1}{\sqrt{3}}j - \frac{1}{\sqrt{3}}k)[/tex]

Therefore, the vector can be expressed as a product of its length and direction as:

|v| u = [tex]\frac{1}{\sqrt{2}}[/tex] [tex](\frac{1}{\sqrt{3}}i - \frac{1}{\sqrt{3}}j - \frac{1}{\sqrt{3}}k)[/tex]

Answer:

D. It is a decimal that terminates after 3 decimal places

I hope this helps!

Answer: False

Natural numbers are not closed under division

Some natural numbers divide to get another natural number. For example, divide 10 over 2 to get 10/2 = 5.

However, there are infinitely many natural numbers that divide to get something that isn't a natural number. Example: 10/7 = 1.43 approximately. All we need is one counterexample to contradict the original statement.

A set is considered closed under division if dividing any two values in that set leads to another value in the set. More formally, if a & b are in some set then a/b must also be in the same set for that set to be closed under division.

If we changed "natural numbers" to "rational numbers", then that set is closed under division. If p, q are rational numbers then p/q is also rational. Basically, dividing any two fraction leads to some other fraction. The value of q cannot be zero.

Answer:

x = -8

Step-by-step explanation:

[tex]6(x - 1) = 9(x + 2)[/tex]

Expand :

[tex]6(x - 1) = 6x - 6 \\ 9(x + 2) = 9x + 18[/tex]

[tex]6x - 6 = 9x + 18[/tex]

Collect like terms and simplify

[tex]6x - 9x = 18 + 6 \\ - 3x = 24[/tex]

Divide both sides of the equation by -3

[tex] \frac{ - 3x}{ - 3} = \frac{24}{ - 3} \\ x = - 8[/tex]

Answer:

Step-by-step explanation:

6x - 6 = 9x + 18

-3x - 6 = 18

-3x = 24

x = -8 is the solution

Answer:

Step-by-step explanation:

[tex]5=\frac{z}{4}-3[/tex]

[tex]\frac{z}{4}-3=5[/tex]

[tex]\frac{z}{4}=5+3[/tex]

[tex]\frac{z}{4}=8[/tex]

[tex]z=8\cdot \:4[/tex]

[tex]z=32[/tex]

Answer:

i think is the second one

Step-by-step explanation:

Answer: 32÷8=4

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Step-by-step explanation:

r+4r=24+1

5r=25

r=25/5

r=5

Answer:

r = 5

Step-by-step explanation:

r + 4r - 1 = 24

r + 4r = 25

5r = 25

r = 5

Answer: Distance = 15km ; Displacement ≅ 11'2km

Step-by-step explanation:

In Physics when we speak of distance we refer to the space traveled that is always measured on the trajectory, while displacement refers to the space from an initial position to a final position regardless of the path. When the path is a straight line, the space traveled is equal to the module of the displacement.

Distance: 5km + 5km + 5km = 15km (Red lines)

Displacement² : (10km)² + (5km)² = 100km² + 25km² = 125km²

Displacement : √125km² ≅ 11'2km  (Blue line)

Answer:

D. 30.5

Step-by-step explanation:

Given that A, B, C, D, and E are collinear,

AE = 38,

BD = 15, since segment BC = CD = DE, therefore

BD = ⅔ of BE

15 = ⅔*BE (substitution)

Solve for BE

Multiply each side by 3

15*3 = ⅔*BE*3

45 = 2*BE

Divide both sides by 2

45/2 = BE

22.5 = BE

BE = 22.5

Find AB:

AB + BE = AE (segment addition postulate)

AB + 22.5 = 38 (Substitution)

AB = 38 - 22.5 (Subtracting 22.5 from each side)

AB = 15.5

Find length of segment AD:

AB + BD = AD (segment addition postulate)

15.5 + 15 = AD (Substitution)

30.5 = AD

AD = 30.5

l=3w

3w(4)=48

12w=48

w=4

l=12

hope it helps

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Answer:

Length is 18; width is 6.

Step-by-step explanation:

The formula for the perimeter of a rectangle is:

[tex]P=2l+2w[/tex]

We are given that the perimeter is 48 feet. We are also told that the length is 3 times the width. In other words:

[tex]l=3w[/tex]

So, substitute this for l and 48 for P. Thus:

[tex]48=2(3w)+2w[/tex]

Distribute:

[tex]48=6w+2w[/tex]

Combine like terms:

[tex]48=8w[/tex]

Divide both sides by 8:

[tex]w=6[/tex]

So, the width is 6.

The length as we know is 3 times the width, so the length is 3(6) is 18.

And we are done!

We can use the points (-4, 0) and (0, 2) to solve.

Slope formula: y2-y1/x2-x1

2-0/0-(-4)

2/4

1/2

Best of Luck!

Answer:

x>18

Step-by-step explanation: