All imaginary numbers can be written as complex numbers in the form a+bi.

For the number 5i,what is the value of a and b?

Group of answer choices

a=5 and b=1

a=5 and b= 0

a=0 and b=5

a=1 and b=5

Answer:

Step-by-step explanation:

Answer:

C. It is not proportional because it is not a straight line.

Step-by-step explanation:

You can check to see if it is a straight line by setting up a table and ensuring that the values increase by the same amount every ordered pair.

------> The Answer Is C <------

Hope this helps have a good day :D

You can use the notation P(A), read “the probability of event B, given event A” to write a conditional probability. The correct answer is C.

Conditional probability refers to the probability of one event occurring given that another event has already occurred. In this case, we are interested in the probability of event B occurring given that event A has already occurred, and we can represent this using the notation P(B|A), where '|' means 'given'.

For example, let's say we are interested in the probability of getting a head on a coin toss (event B), given that the coin was flipped and landed on heads (event A). We could represent this using the notation P(B|A). The value of P(B|A) would be 1, because if the coin already landed on heads, then the probability of getting a head on the next flip is certain.

Conditional probability is an important concept in probability theory and is often used in real-world applications, such as predicting the likelihood of a disease given certain symptoms, or the probability of an event occurring given certain conditions.

The correct answer is C.

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Answer:

Step-by-step explanation:

5*7*5

= 175 combinations.

Deborah has 175 unique outfit combinations to choose from, ensuring she can mix and match her slacks, shirts, and sweaters for variety and style.

Combinations are a fundamental concept in mathematics that allows us to count the different ways we can select items from a given set. In this scenario, Deborah has five pairs of slacks, seven shirts, and five sweaters, and she wants to know how many unique combinations she can create by choosing one pair of slacks, one shirt, and one sweater each day. Let's explore the solution to this problem.

To find the number of combinations, we'll use the concept of the multiplication principle, also known as the counting principle. According to this principle, if we have "n" choices for one item and "m" choices for another item, the total number of combinations is given by the product of these choices, i.e., n x m.

1. For selecting a pair of slacks, Deborah has 5 choices (since she has 5 pairs of slacks).

2. For selecting a shirt, she has 7 choices (due to the 7 shirts available).

3. For selecting a sweater, she has 5 choices (since she has 5 sweaters).

Now, using the multiplication principle, we multiply the number of choices for each item:

Number of combinations = Number of choices for slacks "5" x Number of choices for shirts "7" x Number of choices for sweaters "5".

Number of combinations = 5 x 7 x 5.

Now, we perform the calculations:

Number of combinations = 175.

So, Deborah has a total of 175 different combinations she can create by choosing one pair of slacks, one shirt, and one sweater each day.

In mathematical terms, we can represent this as:

Number of combinations = 5 × 7 × 5 = 175.

This result means that Deborah has 175 unique outfit combinations to choose from, ensuring she can mix and match her slacks, shirts, and sweaters for variety and style.

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Answer:

The scale is 1/60

Step-by-step explanation:

Answer:

he can paint 8 chairs

Step-by-step explanation:

he has 78/10 liters of paint he uses 6/10 which makes it 72/10 and each chair needs 9/10 paint 9 times 8=72

Solution:

Given;

Thus;

ANSWER: f(1.5) = 0

The requried, local minimum and maxium for the given function is √2 and -√2.

We need to find the local maximum and local minimum of the function \(f(x) = 2x + 4x^{(-1)}.\)

First, we find the derivative of f(x):

\(f'(x) = 2 - 4x^{(-2)} = 2 - 4/x^2\)

Setting f'(x) = 0 to find the critical points:

\(2 - 4/x^2 = 0\)

Solving for x, we get:

x = ±√2

To determine whether these critical points are local maxima or minima, we need to examine the sign of the second derivative:

\(f''(x) = 8x^{(-3)}\)

When x = √2, f''(√2) = 8/(√2)³ = 8√2 > 0, so x = √2 is a local minimum.

When x = -√2, f''(-√2) = 8/(-√2)³ = -8√2 < 0, so x = -√2 is a local maximum.

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Answer:

 40

Step-by-step explanation:

you mutiply then take away the 2 last digits

Answer:

Step-by-step explanation:

0.6*3t+0.8*4t=75

so t=15

apple=3t=45

orange=4t=60

Answer: 6 inches long and 4 inches wide

Step-by-step explanation: The dimensions of the actual crate are 20 times those on Jacob's drawing. The dimensions on the builder's drawing are 1/10 of those, so (1/10)(20) = 2 times the dimensions on Jacob's drawing.

hope this helps

Answer:

y = -2x + 1

Step-by-step explanation:

The linear equation is generally written in y = mx + b form. Since m (the value of the slope) is already given, only the value of b must be determined. To do this, plug in x, y, and m for their values in the equation to get:

13 = -2 (-7) + b

Then, simplify.

13 = 14 + b

b = -1

Once you find the b value, plug everything back in and get y = -2x + 1.

Answer: 36 oz box

Step-by-step explanation:

3.1/12=0.258333

7.9/360.291444

Thus, the 36 oz box is the better buy

In the quadratic equation y = a\(x^{2}\) + c ,the value of x = ± \(\sqrt \frac{y-c}{a}\)

A quadratic equation is any equation containing one term wherein the unknown is squared and no term wherein it's far raised to a higher power.

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, in which a and b are the coefficients, x is the variable, and c is the constant term.

To find the value of x

Assuming \(a\neq o\)

First, subtract c from both the sides to get:

\(y-c=ax^{2}\)

then, divide both sides by \(a\) and transpose to get:

\(x^{2} =\frac{y-c}{a}\)

So, \(x\) must be a square root of \(\frac{y-c}{a}\)  and we can deduce:

\(x=\) ± \(\sqrt \frac{y-c}{a}\)

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To find the measure of the geometry-big circle, we need to sum up the measures of all the arcs around the circle.

We are given the following measures:

\(\sf\:m\angle AB = 56 \\\)

\(\sf\:m\angle BC = 59 \\\)

\(\sf\:m\angle CD = 63 \\\)

\(\sf\:m\angle DE = 63 \\\)

\(\sf\:m\angle EF = 31 \\\)

To find the measure of the geometry-big circle, we add up these measures:

\(\sf\:m\angle AB + m\angle BC + m\angle CD + m\angle DE + m\angle EF \\\)

Substituting the given values:

\(\sf\:56 + 59 + 63 + 63 + 31 \\\)

Simplifying the expression:

\(\sf\:272 \\\)

Therefore, the measure of the geometry-big circle is 272.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer: The quotient is 3y² + 2y - 1.

Step-by-step explanation:

You can use long division to solve this expression by setting the dividend under the roof and the divisor outside as you would normally do when dividing numbers.

1) Look at the first term of the dividend, 15y³, and the first term of the divisor, 5y. Determine what value multiplied by 5y would give you 15y³. The answer is 3y², and given the number, you multiply it by the WHOLE divisor.

3y²(5y + 6) = 15y³ + 18y² <-- subtract this from the dividend.

2) Continue this process and make sure to drag down the next term for each new value you form after subtracting. Keep in mind of any negative values! When you reach up to -5y, determine what value multiplied by 5y would give you the value of -5y, which would be -1.

3) You should be left with a remainder of 0, leaving you with a quotient of 3y² + 2y - 1.

Answer:

(21 + 11)2 = 64

So, I don't think teachers do this, but this is my way of doing it

Okay, so first, I divided 64 by 2 :

64 ÷ 2 = 32

Then, I subtracted 11 from 32:

21

Now, to check, just do the problem :

(21 + 11)2 = 64

      32 * 2 = 64

Answer:

The solutions are:

\(m=-3,\:m=-19\)

Step-by-step explanation:

Given the expression

\(\left(m\:+11\right)^2=\:64\)

\(\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\)

solving

\(m+11=\sqrt{64}\)

\(m+11=\sqrt{8^2}\)

\(m+11=8\)        ∵ \(\sqrt{8^2}=8\)

Subtract 11 from both sides

\(m+11-11=8-11\)

Simplify

\(m=-3\)

now solving

\(m+11=-\sqrt{64}\)

\(m+11=-\sqrt{8^2}\)

\(m+11=-8\)      ∵ \(\sqrt{8^2}=8\)

Subtract 11 from both sides

\(m+11-11=-8-11\)    

Simplify

\(m=-19\)

Thus, the solutions are:

\(m=-3,\:m=-19\)

Answer:

89, 178, 267, 356, 445, 534, 623, 712, 801, 890 and so on

Answer:

64

Step-by-step explanation:

Step-by-step explanation:

To solve the problem, we'll use the information given to find the values of A and k in the equation T = 20 + Ae^(-kt), where T is the temperature in degrees Celsius at time t.

a. Finding the value of A:

We're given that the initial temperature of the tea was 70℃. Substituting this into the equation, we get:

70 = 20 + Ae^(0) (since e^0 = 1)

70 - 20 = A

A = 50

So the value of A is 50.

b. Finding the value of k:

We're told that it takes 4 minutes for the tea to decrease in temperature from 70℃ to 50℃. We can use this information to set up an equation and solve for k.

Substituting T = 70 and t = 4 into the equation, we have:

70 = 20 + 50e^(-4k)

Subtracting 20 from both sides:

50 = 50e^(-4k)

Dividing both sides by 50:

1 = e^(-4k)

Taking the natural logarithm (ln) of both sides:

ln(1) = ln(e^(-4k))

0 = -4k

Dividing both sides by -4:

0 = k

However, we need to check if this solution satisfies the condition for the tea to decrease in temperature from 70℃ to 50℃ in 4 minutes.

Substituting T = 50 and t = 4 into the equation, we have:

50 = 20 + 50e^(-4(0))

50 = 20 + 50e^0

50 = 20 + 50(1)

50 = 20 + 50

50 = 70

Since 50 is not equal to 70, the value of k = 0 does not satisfy the given condition.

Let's try another approach:

Substituting T = 50 and t = 4 into the equation, we have:

50 = 20 + 50e^(-4k)

Subtracting 20 from both sides:

30 = 50e^(-4k)

Dividing both sides by 50:

0.6 = e^(-4k)

Taking the natural logarithm (ln) of both sides:

ln(0.6) = ln(e^(-4k))

ln(0.6) = -4k ln(e)

ln(0.6) = -4k(1)

ln(0.6) = -4k

Simplifying further:

k = ln(0.6) / -4

Using a calculator or computer to evaluate ln(3/5) / -4, we get approximately:

k = ln(5/3) / 4

To recap:

a. The value of A is 50.

b. The value of k is approximately k = ln(5/3) / 4

.

Note: The calculations provided are based on the given information and assumptions. If there are any additional details or specific conditions provided, please let me know, and I'll be happy to assist you further.

A function assigns the values. The value of f(-3) and f(3) + f(-3) is 8 and -8, respectively.

A function assigns the value of each element of one set to the other specific element of another set.

Given the function f(x)=-x²-4x+5, therefore, the value of f(x) when the value of x is -3 is,

f(-3) = -(-3)² - 4(-3) + 5

f(-3) = -9 + 12 + 5

f(-3) = 8

Now, the value of f(x) when the value of x is 3 is,

f(3) = -(3)²-4(3)+5

f(3) = - 9 - 12 + 5

f(3) = -16

further, the value of f(3) + f(-3) is,

f(3) + f(-3) = -16 + 8

f(3) + f(-3) = -8

Hence, the value of f(-3) and f(3) + f(-3) is 8 and -8, respectively.

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Properties of Definite Integrals A definite integral is a function that assigns a value to the area under a curve on a given interval are additive , linearity , continuity , monotonicity and upper and lowersums.

1. Additivity: The definite integral of a sum is equal to the sum of the definite integrals.

2. Linearity: The definite integral of a linear function is equal to the product of the function's slope and the length of the interval.

3. Continuity: The definite integral of a continuous function is equal to the area under the curve between two points.

4. Monotonicity: If a function is increasing or decreasing on a given interval, then the definite integral of the function is also increasing or decreasing.

5. Upper and Lower Sums: The upper and lower sums of a function are the sums of the areas of rectangles constructed under or over the curve between two points. The definite integral of the function is equal to the difference between the upper and lower sums.

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The area of the square is given as 100 square unit

You should be aware that the square has all its sides equal

The perpendicular from opposite vertices represent distance

The given vertices are

(2,2) and (10,8)

Using the formula for distance between two points

d=√(10-2)²+(8-2)²

d=√8²+6²

d = √64+36

d=√100

This implies that d=10

The area of a square is given as s²

Area = 10²

Atrea = 100 square units

In conclusion, the area of the square is 100 square units

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Translated question:

The vertices of a square ABCD are A(2,2) and B(10,8), Find the area of the square

Answer:

diana

Step-by-step explanation:

Answer:

I think it’s Diana I’m sorry if I’m wrong :P

Explanation:

We are given the sides are congruent due to the tickmarks. Specifically

TU = WV (single tickmarks)

TV = WX (double tickmarks)

So we just need the "A" of "SAS". The A is between the two S letters, so the angle is between the two sides. For triangle TUV, the angle T is between the two sides with the tickmarks. Similarly, angle W is between the tickmarked sides of triangle WVX.

If we know that angle T = angle W, then we have enough information to use SAS.

The half-life of the radioactive substance is approximately 59.1 hours.

Let's denote the amount of the radioactive substance present at time t by M(t). We know that at time t=0, M(0) = 100 mg.

After 6 hours, the mass decreased by 5%, which means that 95% of the initial mass remains. Therefore, we have:

M(6) = 0.95 x M(0) = 0.95 x 100 mg = 95 mg

We also know that the rate of decay is proportional to the amount of the substance present at time t. This means we can write a differential equation for M(t):

dM/dt = kM

where k is the proportionality constant. The solution to this differential equation is:

M(t) = M(0) e^kt

To find the half-life of the substance, we need to find the value of t for which M(t) = M(0)/2. Substituting this into the equation above, we get:

M(0)/2 = M(0) e^kt

Simplifying and solving for k, we get:

k = ln(1/2) / t1/2

where t1/2 is the half-life of the substance.

Substituting the values we know, we get:

95 = 100 e^6k

Solving for k, we get:

k = ln(95/100) / 6 = -0.0117

Substituting this value of k into the equation for k above, we get:

t1/2 = ln(1/2) / (-0.0117) ≈ 59.1 hours

Therefore, the half-life of the radioactive substance is approximately 59.1 hours.

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Answer: 32

Step-by-step explanation:

     We will use the Order of Operations. First, we will do parentheses (), then brackets [], then lastly the braces {}, then lastly add 12.

Given:

     {[2+(11+9)]-2)+12

Add 11 to 9:

     {[2+20]-2)+12

Add 2 to 20:

     {22-2)+12

Subtract 2 from 20:

     20 + 12

Add 20 and 12:

     32

The slope of the curve  y⁴ = y² - x² is 1 and repeat the process for the second point.

Find the slopes of the curve y⁴ = y² - x² at the given points, we need to differentiate the equation implicitly with respect to x.
Differentiating both sides of the equation with respect to x, we get:
4y³ * (dy/dx) = 2y * (dy/dx) - 2x
Next, we can solve for (dy/dx) by isolating it on one side of the equation:
4y³ * (dy/dx) - 2y * (dy/dx) = -2x
(2y - 4y³) * (dy/dx) = -2x
(dy/dx) = -2x / (2y - 4y³)
Now, substitute the x and y values for each point into the equation to find the slopes at those points.
For example, if one point is (1, 1), we substitute x = 1 and y = 1 into the equation:
(dy/dx) = -2(1) / (2(1) - 4(1)³)
(dy/dx) = -2 / (2 - 4)
(dy/dx) = -2 / -2
(dy/dx) = 1
Repeat the process for the second point, and you will have the slopes of the curve at both points.

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Answer: (-3,-1)

Step-by-step explanation:

Check the picture below.