Find the distance between 2-3i and 9+21i

The veterinarian gave each cat 1/5 of a bottle of medicine. By dividing the total medicine (2/5 of a bottle) by 1/5, we find that there were 2 sick cats.

To find the number of sick cats, we need to divide the amount of medicine given to the cats by the amount given to each cat. Since each cat received 1/5 of a bottle, we can divide the total medicine (2/5 of a bottle) by 1/5 to find the number of cats. This can be done by multiplying the total medicine by the reciprocal of 1/5, which is 5/1.

Therefore, there were 2 sick cats.

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it is an increase of 400%

Final answer:

The percent increase in Minerva's bicycle price is calculated by subtracting the original price from the new price, dividing by the original price, and then multiplying by 100%. The calculation results in a 400% increase.

Explanation:

The percent increase in the price of the bicycle that Minerva bought and sold is calculated using the formula for percent change, which is (New Price - Original Price) / Original Price times 100%. In this case, the original price is $10 and the new price is $50.

To calculate the percent increase:
($50 - $10) / $10 times 100% = $40 / $10 times 100% = 4 times 100% = 400%.

Therefore, the correct answer is 400%, which is option A.

Answer:

-3x

Step-by-step explanation:

Combine like terms (terms with the same amount of variables). Note that + x = + 1x. First add, then subtract:

2x + x = 3x

3x - 6x = -3x

-3x is your answer.

~

Answer:

6x

Step-by-step explanation:

Answer: You can use this to help you out:

Determine the term life insurance amount per thousand on a 20-year-old male for a 10-year policy given that the face value of the policy is $65,000 and the annual premium is $291.85.

a.

$0.00449

c.

$0.2227

b.

$4.49

d.

$222.72

First find how many thousands on the amount of the face value

You do that by dividing the amount of the face value by 1000

65,000÷1,000=65

So the term life insurance amount per thousand is

291.85÷65=4.49...answer

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Answer:

a.  $1,377.20

Step-by-step explanation:

To determine the annual premium for the policy, you have to divide the face value by 1,000:

$55,000/1,000= $55

Then, you have to multiply this result for the rate found on the table, which according to the information given is $25.04:

$55*$25.04= $1,377.20

The annual premium for the policy is $1,377.20.

You can use the pythagorean theorem to find the side lengths. One is a straight line and it's 7 units. I'll attach a picture of what this looks like, but the side lengths of the other ones are √37 and √72. Add these up to get the perimeter → 21.568 or 21.6 units.

Answer: B. y = 1.560x - 4.105*****

Answer:

Option B.

Step-by-step explanation:

The general equation of best fit line is

[tex]y=mx+b[/tex]              .... (1)

where, m is slope and b is y-intercept.

[tex]m=\frac{\sum_{i=1}^nx_iy_i-n\overline{x}\overline{y}}{\sum_{i=1}^nx_i^2-n\overline{x}^2}[/tex]

[tex]b=\overline{y}-b\overline{x}[/tex]

Using the graphing calculator we get

[tex]m=1.56015\approx 1.560[/tex]

[tex]b=-4.10526\approx -4.105[/tex]

Substitute m=1.560 and b=-4.105 in equation (1).

[tex]y=1.560x-4.105[/tex]

The equation of the line of best fit for the following data y = 1.560x - 4.105.

Therefore, the correct option is B.

Answer:

f(x)⁻¹ = x³ + 2

Step-by-step explanation:

Find the inverse of f(x) = ∛(x - 2).

The first step is to let f(x) = y

y =  ∛(x - 2)

Then make x the subject of the formula

y³ =  [∛(x - 2)]³

y³ = x - 2

x = y³ + 2

∴ f(x)⁻¹ = y³ + 2

Replacing y with x we have.

f(x)⁻¹ = x³ + 2

Answer:

Step-by-step explanation:

Triple 15 = p

Answer:

he spent $135

Step-by-step explanation:

He spent $135

1. 0.6(600)=360

2. 0.375(360)=135

A = sinx - sin3x,  

B = -sin3x + sin5x  

First A:  

The average of x and 3x is 2x, and they (x and 3x, that is) are each a distance of x from this average. That's fancy talk for:  

x = 2x-x,  

3x = 2x+x.  

So, A = sin(2x-x) - sin(2x+x)  

Using angle sum formulas:  

A = (sin2x cosx - cos2x sinx) - (sin2x cosx + cos2x sinx)  

A = -2 cos2x sinx  

Similarly,  

B = -sin(4x-x) + sin(4x+x)  

= -(sin4x cosx - cos4x sinx) + (sin4x cosx + cos4x sinx)  

B = 2 cos4x sinx  

Now,  

sinx - 2sin3x + sin5x = A+B = -2 cos2x sinx + 2 cos4x sinx  

= 2 sinx (cos4x - cos2x).  

Sinx-2sin3x+sin5x=2sinx(cos4x-cos2x)  

sinx - 2sin3x + sin5x = sinx - sin(3x) + sin(5x)- sin(3x)

=  2· cos[(x+3x)/2] · sin[(x-3x)/2] + 2·cos[(5x+3x)/2]· sin[(5x-3x)/2]

= 2· cos(2x) ·sin(-x) + 2· cos(4x) · sin(x)

=  -2·cos(2x)·sinx + 2· cos(4x)·sinx

=  2·sinx · [ cos(4x)- cos(2x)]

Answer:

C

Step-by-step explanation:

F must be on -4

H must be on 4 (because it is -f=-(-4)=-1•-4=4)

Answer:

Step-by-step explanation:

the answer is c

The solution to the given equation is x = -7/9, after simplifying and solving for x.

To simplify the equation -4(x + 4x) = 2(2 - x) + 10, start by combining like terms within the parentheses: -4(5x) = 2(2 - x) + 10. This leads to -20x = 4 - 2x + 10. Further simplifying, you get -20x = 14 - 2x. Now, add 2x to both sides to eliminate the variable on the right, resulting in -18x = 14. To isolate x, divide both sides by -18, yielding x = -14/18, which can be further reduced to x = -7/9. In summary, the equation simplifies to x = -7/9 after a series of steps.

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Answer: First option

Step-by-step explanation:

By definition, you know that:

[tex]55\°=\frac{170\°-x}{2}[/tex]

Therefore, to calculate the measure of the missing angle, you must solve for x, as you can see below:

- Multiply both sides of the equation by 2.

- Subtract 170 from both sides of the equation.

- Multiply both sides of the equation by -1

Therefore:

[tex]55\°=\frac{170\°-x}{2}\\\\(2)55\°=\frac{170\°-x}{2}(2)\\\\110\°=170\°-x\\110\°-170\°=170\°-x-170\°\\(-1)-60\°=-x(-1)\\x=60\°[/tex]

Da la answer is 60

Step-by-step explanation:

Gradpoint approved

[tex]\huge\boxed{\text{Greatest common factor}}[/tex]

The greatest common factor is the greatest number that both [tex]44[/tex] and [tex]12[/tex] are divisible by. In this case, it is [tex]4[/tex]. Each number can then be divided by the greatest common factor using the reverse of the distributive property.

Answer:

Their sign changes.

For this case we have to:

Given two lines:

[tex]y_ {1} = m_ {1} x_ {1} + b_ {1}\\y_ {2} = m_ {2} x_ {2} + b_ {2}[/tex]

By definition, if both lines are perpendicular to each other, then the product of their slopes is -1. That is to say:

[tex]m_ {1} * m_ {2} = - 1[/tex]

ANswer:

The product of the slopes of two perpendicular lines is -1.

Answer:

[tex]106\°+x=180\°[/tex]

Step-by-step explanation:

Observing the figure

we know that

[tex]106\°+x=180\°[/tex] ----> by supplementary angles

Solve for x

[tex]x=180\°-106\°=74\°[/tex]

Answer:

24 outfits

Step-by-step explanation:

Since you have 4 choices of shirts, then 3 choices of shorts, and then 2 choices of shoes, the formula should be set up as 4 x 3 x 2. This gives you 24 outfit options.

Answer:

The Second Option is your Answer ( Option 2)

Step-by-step explanation:

1) proof ( replace h with -2)

|-2-2| = 4

|-4| = 4

2) proof ( replace h with 6)

|6-2| = 4

|4|=4

Hopes this helps !

Answer:

[tex]h = -2\\h = 6[/tex]

Step-by-step explanation:

The absolute value is a function that transforms any value x into a positive number.

Therefore, for the function [tex]f(x) = |x|[/tex]  x> 0 for all real numbers.

Then the equation:

[tex]|h-2| = 4[/tex] has two cases

[tex](h-2) = 4[/tex]    if [tex]h > 2[/tex]  (i)

[tex]-(h-2) = 4[/tex]    if [tex]h < 2[/tex] (ii)

We solve the case (i)

[tex]h = 4 + 2\\h = 6[/tex]

We solve the case (ii)

[tex]-h +2 = 4\\h = 2-4\\h = -2[/tex]

Then the solution is:

[tex]h = -2[/tex] or [tex]h = 6[/tex]

➷ 236 + 542 = 778

778 + N = 863

Subtract 778 from both sides:

N = 85

➶ Hope This Helps You!

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➶ Have A Great Day ^-^

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Answer:

85

Step-by-step explanation:

(236+542)+N=863 add the parenthesis first which gives you 778 subtract 778 by 863 which gives you 85 therefore your answer is 85

Answer: 69%

Step-by-step explanation:

16820x100= 1682000

1682000÷24365=69.033

Answer:A-1/2h(b1+b2)

A-1/2*(10.1)*(30.5+21.4)

A-3296.135 i think

Step-by-step explanation:

To find the area of the unshaded portion of a figure containing a trapezoid and a rhombus, calculate the area of each figure first using their respective formulas. Subtract the area of the overlapping (shaded) region from the total to find the area of the unshaded portion.

The problem asks to find the area of the unshaded portion of a figure, which includes a trapezoid and a rhombus. Since we don't have the specific values of the sides and heights of each figure, a general approach would be to calculate the area of each figure first, then subtract the area of the shaded (overlapping) region from it.

The formula for the area of a trapezoid is A = 1/2 (a+b)h, where 'a' and 'b' are the lengths of the parallel sides and 'h' is the height. For the rhombus, the formula is A = 1/2 (d1 * d2), where 'd1' and 'd2' are the diagonals.

Assuming you can measure and determine the shaded region, you would compute its area as well and subtract this from the total of the previous two calculations. This would give you the area of the unshaded portion.

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Answer:

you multiply all three of these numbers to get an answer of 450

Step-by-step explanation:

Final answer:

The volume of the shoe box is calculated using the formula for the volume of a rectangular prism, resulting in a total of 450 cubic inches.

Explanation:

The formula for finding the volume of a rectangular prism (which is the shape of a shoe box) is Volume = Length × Width × Height. However, before calculating, we need to ensure all dimensions are in the same unit. Since the given width is in mixed number form, we will convert 6 2/3 inches to an improper fraction which is 20/3 inches. We then multiply the length, width, and height.

Volume = (13.5 inches) × (20/3 inches) × (5 inches)
Volume = (13.5 × 20/3 × 5) cubic inches
Volume = (270/3 × 5) cubic inches
Volume = (90 × 5) cubic inches
Volume = 450 cubic inches

The shoe box's volume is 450 cubic inches.

Answer:

5.7 times

Step-by-step explanation:

To find out how much ribbon is left after using 1/2 yard from a piece that is 7/8 yard long, convert 1/2 yard to 4/8 and subtract from 7/8, leaving you with 3/8 yard of ribbon remaining.

To determine how much ribbon will remain after using 1/2 yard for a craft project from a piece that measures 7/8 yard, you need to subtract the amount used from the total length you have. Since we are working in yards, ensure both amounts are in the same units. Here are the steps to find the remaining ribbon:

Start with the total length of ribbon: 7/8 yard.

Subtract the length of ribbon used for the project: 1/2 yard.

Convert 1/2 yard to an equivalent fraction with a denominator of 8, which is 4/8 yard.

Subtract 4/8 yard from 7/8 yard to find the remaining length.

7/8 yard - 4/8 yard = 3/8 yard remaining.

So, after using 1/2 yard of ribbon for a craft project, you will have 3/8 yard of ribbon left from the original 7/8 yard piece.

Answer:

Relation.

Step-by-step explanation:

This is a relation but not a function. The input -1 maps to both 0 and 2; this is a one-to-many relation  so it is not a function. Functions are either one-to-one or many-to-one.

Answer:

Relation cause its not a function

Step-by-step explanation:

This is a relation but not a function.

Answer:

The explanation in the procedure

Step-by-step explanation:

we know that

[tex]1\ ft=12\ in[/tex]

In this problem is correct to use the measurement [tex]8\ ft\ 4\ in[/tex] instead of [tex]7\ ft\ 16\ in[/tex]  

because

[tex]16\ in=12\ in+4\ in=1\ ft+4\ in[/tex]

therefore

[tex]7\ ft\ 16\ in=7\ ft\ +1\ ft+4\ in=8\ ft\ 4\ in[/tex]

Answer: The answer is C

Step-by-step explanation:

Answer:

Option C is correct.

Step-by-step explanation:

C. Buying a hammer and buying nails are dependent events. - This is correct.

Two events are said to be dependent on each other, if the occurrence of the first event affects the occurrence of the second event thus changing the probability. Here the probability for both the events is [tex]0.10\times0.40=0.04[/tex]

Answer:

2d + 8

Step-by-step explanation:

twice the number d = 2 × d = 2d and 8 more means add on 8, that is

2d + 8 ← is the variable expression

(d x 2) + 8

deconstruct it from the end of the sentence- twice the number 'd' and add 8