Please help due in 30 mins

Step-by-step explanation:

(4-7i)-(-3+6i)

4-7i+3-6i

7-13i(simplified)

Answer:

7-13i

Step-by-step explanation:

(4-7i) - (-3+6i)

4-(-3)+(-7-6)i

7-13i

Answer:

Slope=1.000/2.000=0.500

b-i

q-i

b-(2*q+6)=0

Step-by-step explanation:

1.1     Solve   b-2q-6  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  b-2q-6  = 0 and calculate its properties

Notice that when b = 0 the value of q is 3/-1 so this line "cuts" the q axis at q=-3.00000

 q-intercept = 6/-2 = 3/-1  = -3.00000

When q = 0 the value of b is 6/1 Our line therefore "cuts" the b axis at b= 6.00000

 b-intercept = 6/1  =  6.00000

Slope is defined as the change in q divided by the change in b. We note that for b=0, the value of q is -3.000 and for b=2.000, the value of q is -2.000. So, for a change of 2.000 in b (The change in b is sometimes referred to as "RUN") we get a change of -2.000 - (-3.000) = 1.000 in q. (The change in q is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     =  1.000/2.000 =  0.500

 Slope = 1.000/2.000 = 0.500

 b-intercept = 6/1 = 6.00000

 q-intercept = 6/-2 = 3/-1 = -3.00000

Answer:

C.

Step-by-step explanation:

Hope this helps :)

Answer:

The point-slope form of the equation of the perpendicular line that goes through (5, 0) is:

Step-by-step explanation:

Given the equation

\(y=2x-1\)

comparing the equation with the slope-intercept form

\(y=mx+b\)

Here,

so the slope of the line is 2.

As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line, so

The slope of the perpendicular line will be: -1/2

Therefore, the point-slope form of the equation of the perpendicular line that goes through (5, 0) is:

\(y-y_1=m\left(x-x_1\right)\)

\(y-0=\frac{-1}{2}\left(x-5\right)\)

\(y=\frac{-1}{2}\left(x-5\right)\)

\(\:y=-\frac{1}{2}x+5\cdot \:\frac{1}{2}\)

\(y=-\frac{1}{2}x+\:\frac{5}{2}\)

Answer:

8 38/48

Step-by-step explanation:

To prove the statement that 3 divides (n³ + 5n + 6) for any integer n ≥ 20 using mathematical induction, we will show that the statement holds for the base case (n = 20) and then assume it holds for an arbitrary value of n and prove it for (n + 1).

Base case (n = 20):

Substitute n = 20 into the expression (n³ + 5n + 6):

(20³ + 5 * 20 + 6) = 9266

Since 9266 is divisible by 3 (9266 = 3 * 3088), the statement holds for the base case.

Inductive step:

Assume that the statement holds for an arbitrary value of n, denoted as k, i.e., 3 divides (k³ + 5k + 6).

Now we need to prove that the statement holds for (k + 1), i.e., 3 divides ((k + 1)³ + 5(k + 1) + 6).

Expand the expression ((k + 1)³ + 5(k + 1) + 6):

(k³ + 3k² + 3k + 1 + 5k + 5 + 6) = (k³ + 5k + 6) + (3k² + 3k + 6)

By the induction hypothesis, we know that (k³ + 5k + 6) is divisible by 3. Now we need to show that (3k² + 3k + 6) is also divisible by 3.

Factoring out 3 from (3k² + 3k + 6), we get: 3(k² + k + 2).

Since k² + k + 2 is an integer, we conclude that (3k² + 3k + 6) is divisible by 3.

Therefore, the statement holds for (k + 1).

By the principle of mathematical induction, we have shown that the statement "3 divides (n³ + 5n + 6)" holds for any integer n ≥ 20.

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Answer:

The money saved is $153-$147= $6

Step-by-step explanation:

Science center tickets are 3 for $36.75

so 12 tickets costs =4*36.75=$147

and zoo tickets are 4 for $51

so 12 tickets costs =3* 51=$153

The money saved is $153-$147= $6

Three unit fractions whose sum is 1/2 is: 1/6, 1/6 and 1/6.

Unit fractions are any fractions with 1 as the numerator. We only use one portion of the total, which is divided into an infinite number of pieces in these fractions. Unit stands for one. They are referred to as unit fractions as a result. For instance, if Joseph is eating one portion of a pizza that has been divided into 8 equal pieces, that portion will be denoted as 1/8, which is a unit fraction.

Given that the number to be formed is 1/2.

The unit fraction 1/6 can be added three times to get 1/2.

That is,

1/6 + 1/6 + 16 = 3/6 = 1/2

Hence, the three unit fractions whose sum is 1/2 is 1/6, 1/6, and 1/6.

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Answer:

y = - \(\frac{4}{5}\) x - 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (0, 12) and (x₂, y₂ ) = (10, 4)

m = \(\frac{4-12}{10-0}\) = \(\frac{-8}{10}\) = - \(\frac{4}{5}\) ← slope of line L

Parallel lines have equal slopes , then

y = - \(\frac{4}{5}\) x + c ← is the partial equation

To find c substitute (5, - 11) into the partial equation

- 11 = - 4 + c ⇒ c = - 11 + 4 = - 7

y = - \(\frac{4}{5}\) x - 7 ← equation of parallel line

The equation of the straight line which is parallel to L and passes through the point (5 , -11) will be;

⇒ y = - 4/5x - 7

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The straight line L passes through the points (0 , 12) and (10 , 4).

And, The equation of the straight line which is parallel to L and passes through the point (5 , -11).

Now,

Since, The straight line L passes through the points (0 , 12) and (10 , 4).

So, Equation of line L is,

⇒ y - y₁ = (y₂ - y₁) / (x₂ - x₁) (x - x₁)

⇒ y - 12 = (4 - 12) / (10 - 0)  (x - 0)

⇒ y - 12 = - 8 / 10x

⇒ 10 (y - 12) = - 8x

⇒ 10y - 120 = - 8x

⇒ 10y = - 8x + 120

⇒ y = - 8/10x + 12

⇒ y = - 4/5x + 12

And, The equation of the straight line which is parallel to L and passes through the point (5 , -11).

So, We need to find the slope of the line.

Since, The slope of the parallel line is same.

Hence, Slope of the line is,

y = -4/5x + 12

m = dy/dx = - 4/5

m = - 4/5

Thus, The equation of line with slope 1- 4/5 is,

⇒ y - (-11) = - 4/5 (x - 5)

⇒ y + 11 = - 4/5 (x - 5)

⇒ 5 (y + 11) = - 4x + 20

⇒ 5y + 55 = - 4x + 20

⇒ 5y = - 4x + 20 - 55

⇒ 5y = - 4x - 35

⇒ y = - 4/5x - 7

Thus, The equation of the straight line which is parallel to L and passes through the point (5 , -11) will be;

⇒ y = - 4/5x - 7

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Answer:

7/8

Step-by-step explanation:

1/4= 2/8

2/8 + 5/8 = 7/8

For a pack of 52 cards, two cards are drawn together, the probability that one card is clubs and one card is spades is equals to the

\(= \frac{13}{102}\)

Probability is chances of occurrence of an event. It is calculated by dividing the favourable response to the total possible outcomes. We have a pack of 52 cards. Let's consider an event E : card is one card is culb and one is spade

Total possible outcomes = 52

Two cards are drawn together from a pack. So, number of total possible outcomes for drawing two cards from a pack, n(T) = ⁵²C₂ = 1326

In a 52 cards pack, number of spades = 13

Number of clubs cards in pack = 13

Number of ways of choosing/drawing one spades card out of 13 and one one clubs out of 13 cards, n(E) = 169

Probability that one card is clubs and one card is spades on drawing two cards,

\( P(E) = \frac{ n(E)}{n(T)}\)

\(= \frac{169}{1326}\)

\(= \frac{13}{102}\)

Hence, required probability value is \(= \frac{13}{102}\).

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Answer:

I think it goes in this order

<LNO<NLM <OLN

Answer:

<LNO<NLM <OLN

Step-by-step explanation:

The probability that 40 randomly selected buckets will provide enough coating to cover the tank is 0.5000 or 0.5000 (approx) or 0.5000

Given: The surface area of the tank is 80,000 square feet. The coating comes in five-gallon buckets. The area that the coating in one randomly selected bucket can cover varies, with a mean of 2000 square feet and a standard deviation of 100 square feet.

The probability that 40 randomly selected buckets will provide enough coating to cover the tank. (If it matters, you may assume that the selection of any given bucket is independent of the selection of any and all other buckets.)

The area covered by one bucket follows a normal distribution, with a mean of 2000 and a standard deviation of 100. So, the area covered by 40 buckets will follow a normal distribution with a mean μ = 2000 × 40 = 80,000 and a standard deviation σ = √(40 × 100) = 200.

The probability of the coating provided by 40 randomly selected buckets will be enough to cover the tank: P(Area covered by 40 buckets ≥ 80,000).

Z = (80,000 - 80,000) / 200 = 0.

P(Z > 0) = 0.5000 (using the standard normal table).

Therefore, the probability that 40 randomly selected buckets will provide enough coating to cover the tank is 0.5000 or 0.5000 (approx) or 0.5000 (rounded to four decimal places).

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Answer:

P = Rs2500

Step-by-step explanation:

Given that,

Amount, A = Rs 3025

Rate, r = 10%

Let time, t = 2 years

We need to find the sum if the amount is compounded annually. Using the formula of compound interest.

\(A=P(1+\dfrac{r}{100})^n\\\\P(1+\dfrac{10}{100})^2=3025 \\\\P(1.21)=3025\\\\P=\dfrac{3025}{1.21}\\\\P=\text{Rs}\ 2500\)

So, the sum of money is Rs 2500.

The solution to the equation is all real numbers.

Now, let's look at the equation you provided: sec²(θ) (1 - sin²(θ)) = 1. This equation involves the secant and sine trigonometric functions. To solve this equation, we can use some trigonometric identities and algebraic manipulations.

First, we can use the identity 1 - sin²(θ) = cos²(θ) to simplify the left-hand side of the equation. So, we get:

sec²(θ) cos²(θ) = 1

Next, we can use the identity sec²(θ) = 1/cos²(θ) to replace sec²(θ) in terms of cos²(θ). So, we get:

1/cos²(θ) cos²(θ) = 1

Simplifying further, we get:

1 = 1

This means that the equation is true for any value of θ.

In conclusion, solving trigonometric equations involves using various trigonometric identities and algebraic manipulations to simplify the equation and find a solution. In this case, we used the identities 1 - sin²(θ) = cos²(θ) and sec²(θ) = 1/cos²(θ) to simplify the equation and arrive at the solution that all real numbers satisfy the equation.

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Complete Question:

Solve the equation: sec²(θ) (1 - sin²(θ)) = 1

Answer:

Jacqueline = 150 minutes

Cassie = 125 minutes

The answer would be 2. (The difference in length between Cassie’s longest and shortest practice sessions was greater than the difference in length between Jacqueline’s longest and shortest sessions.)

Step-by-step explanation: Cassies longest session was 50 minutes. her shortest session was for 15 minutes and they are 45 minutes apart. Jacquelines longest session was 45 minutes and her sgortest was 30 minutes they are onlu 15 minutes away from eachother so the second answer is correct.

Answer:

c

Step-by-step explanation:

Answer:

A?

Step-by-step explanation:

Answer:

90 minutes

Step-by-step explanation:

it will take twice as long therefore 90 minutes

she sold 2 trays, and each tray contains 12 meat slices and 19 cheese slices

Explanation

Step 1

Let

Each party tray contained the same number of meat slices,so

the total number of party trays and slices of meat and cheese Doris sold is

it means she sold 2 trays, and each tray contains 12 meat slices and 19 cheese slices

I hope this helps you

Answer:

B. 9)8

9 on the outside, 8 on the inside.

Step-by-step explanation:

8/9 is 8÷9, you read it from the top down.

Using the little division "house" from elementary school, the "number getting divided is inside the "house". The "divided by_" is the number on the outside.

The actual math vocabulary is:

Dividend is the number getting divided (on top of a fraction or inside the "house")

Divisor is the "divided by_", bottom of a fraction or the number outside the "house"

Quotient is the answer of a division problem.

The rate of change of the area of the triangle is 7cm/sec when the base is 4cm and height is 7cm.

We know that,

The Base is growing at the rate of 1 cm per sec.

Height is growing at the rate of 2 cm per sec.

Area of triangle: 1/2 × b × h

The rate of change will be:

1/2 × b × h

1/2 × 4/1 × 7/2

28/4

7 cm per sec

Therefore, the rate of change of the area of the triangle is 7cm/sec when the base is 4cm and height is 7cm.

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It is true that the slope of the horizontal tangent line to the parametric curve at a point (x(t), y(t)) is given by dy/dx = (dy/dt)/(dx/dt).

The statement is saying that if f(g(t)) has a horizontal tangent at t = 1, then the curve has a well-defined tangent line at that point, which is also a horizontal tangent. Let's break this down step by step:

f(g'(1)) = 0: This means that the derivative of f with respect to its input g(t) is equal to zero at t = 1. In other words, the slope of the tangent line of f(g(t)) at t = 1 is zero.

dx/dt is not zero at t = 1: This means that the curve g(t) has a well-defined tangent line at t = 1, because the slope of the tangent line of g(t) is not infinite (i.e., the derivative dx/dt is defined and finite).

Setting dy/dx = 0 gives dy/dt / dx/dt = 0: This is using the chain rule of differentiation to relate the derivative of f with respect to t (i.e., dy/dt) to the derivative of f with respect to x (i.e., dy/dx) and the derivative of g with respect to t (i.e., dx/dt).

dy/dt = 0 when dx/dt is not zero: Since dy/dx = 0 and dx/dt is not zero, we can conclude that dy/dt must also be zero at t = 1. This means that the slope of the tangent line of f(g(t)) is also zero at t = 1.

Therefore, the curve has a horizontal tangent at t = 1: Since both g(t) and f(g(t)) have horizontal tangents at t = 1, we can conclude that the curve f(x) also has a horizontal tangent at x = g(1). This means that the tangent line to the curve at that point is horizontal.

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Answer:

Your answer is 196000000

Step-by-step explanation:

The product of 3500 and 5.6 x 10⁴ in scientific notation will be;

⇒ 19.6 × 10⁷

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The expression is,

⇒ 3500 × 5.6 × 10⁴

Now,

Since, The expression is,

⇒ 3500 × 5.6 × 10⁴

After multiply, we get;

⇒ 19,600 × 10⁴

⇒ 19.6 × 10³ × 10⁴

⇒ 19.6 × 10⁷

Thus, The product of 3500 and 5.6 x 10⁴ in scientific notation = 19.6 × 10⁷

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=>10x+2=128°

=>10x=128-2

=>10x=126

=>x=126/10=63/5

=>x=12.6°

Answer:

X = 5

Step-by-step explanation:

1. first, remember that it is a straight Angle.

straight angles always add up to 180.

Equation should be -

10x+2 +128= 180

so you are solving for X

Add 128  and 2=  130

subtract 130 on both sides

2. You remain With 10x=50

Then You divide 50/10

you get 5

3. If You would like, Try checking This answer.

10x+2

when x= 5  

10x5 +2 +128 = 180  

5 =x

I hope helps!

have a wonderful Day!

The correct definition for the given words are shown below:

The aforementioned terms are all used in logical analysis except for terms like geometry, intuition and deductive reasoning.

The logical analysis is done after a premise has been made and then a conclusion would be validated.

For example, if a person says, Last Monday, my shoe tore, so next Monday, my shoe will tear", he is making use of inductive reasoning even though the premise is faulty and he just committed fallacy.

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Answer:

y=2x+3

Step-by-step explanation:

_2y=-4x-12 and than divide dy -2 so it will be Y=2x+3.

Part A - Option C is the best scale for the line plot.

Part B - There will be more dots above the point 1 1/2 than above the point 1/2.

Part A:

Without additional information about the data being plotted, it is difficult to definitively choose the best scale for the line plot. However, in general, a scale that includes all the data points with evenly spaced intervals tends to be the most effective.

Option A includes all the data points but the intervals are not evenly spaced, which can make it difficult to compare the values of the data points. Option B has evenly spaced intervals but it excludes the value 1, which may be important information depending on the context. Option C has evenly spaced intervals and includes all the data points, making it a good option. Option D includes all the data points but has unevenly spaced intervals.

Part B:

Based on the scale chosen in Part A, there will be one dot above the point 1 and there will be two dots above the point 1 1/2. Additionally, there will be more dots above the point 1 1/2 than above the point 1/2.

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