The area of triangle ABC is 84 square units. If AC= 14 units, what is the length of BD, in units ?

Answer:

[tex]\textsf{C)} \quad 11-60i[/tex]

Step-by-step explanation:

[tex]\textsf{Multiply }\: (6-5i)^2[/tex]

[tex]\implies (6-5i)(6-5i)[/tex]

[tex]\implies 6(6-5i)-5i(6-5i)[/tex]

[tex]\implies 36-30i-30i+25i^2[/tex]

[tex]\implies 36-60i+25i^2[/tex]

[tex]\textsf{Remember that }i^2=-1:[/tex]

[tex]\implies 36-60i+25(-1)[/tex]

[tex]\implies 36-60i-25[/tex]

[tex]\implies 36-25-60i[/tex]

[tex]\implies 11-60i[/tex]

Answer: 50,001²-49,999²=0,2.

Step-by-step explanation:

[tex]50,001^2-49,999^2=(50,001+49,999)*(50,001-49,999)=100*0,002=0,2.[/tex]

Answer:

C

Step-by-step explanation:

let f(x)=y and g(x)=x

so y=x²

if y-2=(x-2)

y=x

Answer:

Step-by-step explanation:

2. Given a point with integral coordinates (a, b):

   Vertical line that contains (a, b):

       So here it's not to hard, all you have to understand, is what a vertical line is. If you were to draw a vertical line, you would notice that the x-values remain constant, and the only thing that changes is the y-value. So you're going to have an equation as such: x=a, where a is some constant value, and y is literally anything. So in this case b doesn't matter. The only thing that matters is that x=a. Which is the equation. As long as x is equal to a, it should pass through (a, b)

   Horizontal line that contains (a, b):

       So this is very similar to the vertical line, as one of the values is constant, although the variable that's constant is different. If you were to draw a horizontal line, you would notice the x is changing, but the y-value isn't. This means the y is going to equal to constant value, which may look something like: y=b, which is the equation in this case, since as long as y=b, then the x should at some point equal a on the horizontal line

Why is it impossible to write the equation of a vertical line in slope-intercept form:

   As mentioned before, in a vertical line, the only thing that varies is the y-value, so if you wrote a vertical line as such: y=mx+b, then the x-value would have to vary. But if we were to put restrictions on the equation so that x can only equal some constant value, that means y would only be one point, but if you draw a vertical line, you would know that the y-value is all real numbers (unless of course you put some range restriction), but even then it's going to be more than one number. The other thing is to write an equation in slope-intercept form, you need to know the slope. which is defined as [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]. and by definition a vertical line only varies in y-values and not x. The value of x is defined in the constant equation: x=a. So the slope would be defined as: [tex]\frac{y_2-y_1}{a-a} = \frac{y_2-y_1}{0} = \text{undeefined}[/tex] ("I typed undefined wrong intentionally since it won't let me type it for some reason"). anyways the point is you can divide by 0. So main takeaways: the x-value can't vary, the formula has to output all real numbers for the y-value (unless some range restriction), the slope will have 0 as the denominator since x doesn't vary meaning x_2 - x_1 will = 0, because x_2 = x_1 (because x doesn't vary)

Given an equation in point slope form, explain how to determine the coordinate of the y-intercept:

   There are two ways to do this. The point slope form is expressed as such: y-a = m(x-b). But the m can be distributed so the equation becomes y-a = mx-mb and then add "a" to both equations to get y=mx -mb+a, in this case (0, -mb+a) will be the y-intercept, because if you plug in x as 0, mx will become 0 and it will leave these two values. You could also just of course plug in 0 as x in the point slope intercept form: y-a = m(x-b) and then solve for y. This gives the same result as it simplified to y-a = m(-b) which becomes y-a=-mb which then becomes y=-mb+a.

Answer:

13400 m

Step-by-step explanation:

The slope is defined as:

[tex]Slope=\frac{Rise}{Run}[/tex]

Substitute slope=13.4, Run=1 km=1000 m :

[tex]13.4=\frac{Rise}{1000}[/tex]

Solve for Rise:

[tex]Rise=13.4\cdot 1000=13400 ~m[/tex]

The solution of the equation is given by (-2,-1), This is represented by option C.

A system of equations is a set of equation that have a common solution.

The solution of the equations can be determined by using the Elimination and Substitution method

3x-5y = -1

2x-y = -3

-7x = 14

x = -2

Substituting this value in the equation

3 * (-2) -5y = -1

-6 -5y = -1

-5y = 5

y = -1

Therefore, the solution of the equation is given by (-2,-1), This is represented by option C.

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The probability that a randomly selected cable repair visit will take at least 43 minutes will be 88%.

Given: The times required for a cable company to fix cable problems in its customers' homes are uniformly distributed between 40 minutes and 65 minutes.

It can be deduced that the probability that a randomly selected cable repair visit will take at least 43 minutes will be calculated thus:

= 1 - [(43 - 40)/(65 - 40)

= 1 - 0.12

= 0.88

Hence, The probability that a randomly selected cable repair visit will take at least 43 minutes will be 88%.

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The inverse of the given function is y = (12-x)/6

Given the following function expressed as:

f(x) = -6x +1/2

Replace y with x

x = -6y + 1/2

Make y the subject of the formula

6y = -x + 12

y = (12-x)/6

Hence the inverse of the given function is y = (12-x)/6

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Answer:

24-100, 12-5-22, -4, 37

Step-by-step explanation:

Step-by-step explanation:

what is the question. what am I to do with those random numbers without a question, I'm just writing all this because they said at least 20 characters so don't get offended but pls give a detailed question

The equations of the perpendicular lines are: y = 1/2x + 6, y = 15, y = -x - 2, y = 6x + 3 and y = 1/3x - 4

When a linear equation is represented as:

Ax + By = C

The slope (m) is:

m = -A/B

When the linear equation is represented as:

y = mx + c

The slope is m

A line perpendicular to a linear equation that has a slope of m would have a slope of -1/m

Using the above highlights, the equations of the lines are:

6. y = -2x + 5; (2, 7)

The slope is:

m = -2

The perpendicular slope is:

n = 1/2

The equation of the perpendicular line is:

y = n(x - x1) + y1

This gives

y = 1/2(x - 2) + 7

Evaluate

y = 1/2x - 1 + 7

This gives

y = 1/2x + 6

7. y = -5; (11, 15)

The slope is:

m = 0

The perpendicular slope is:

n = 1/0 = undefined

The equation of the perpendicular line is:

y = n(x - x1) + y1

This gives

y = 15

8. Graph ; (-12, 10)

The slope is:

m = (y2 - y1)/(x2 - x1)

Using the points on the graph, we have:

m = (2 - 3)/(3 - 4)

m = 1

The perpendicular slope is:

n = -1

The equation of the perpendicular line is:

y = n(x - x1) + y1

This gives

y = -1(x + 12) + 10

y = -x - 12 + 10

Evaluate

y = -x - 2

9. y = -1/6x + 1; (-2, -9)

The slope is:

m = -1/6

The perpendicular slope is:

n = 6

The equation of the perpendicular line is:

y = n(x - x1) + y1

This gives

y = 6(x + 2) - 9

Evaluate

y = 6x + 12 - 9

This gives

y = 6x + 3

10. 6x + 2y = 14; (12, 0)

The slope is:

m = -6/2

m = -3

The perpendicular slope is:

n = 1/3

The equation of the perpendicular line is:

y = n(x - x1) + y1

This gives

y = 1/3(x - 12) + 0

Evaluate

y = 1/3x - 4

Hence, the equations of the perpendicular lines are: y = 1/2x + 6, y = 15, y = -x - 2, y = 6x + 3 and y = 1/3x - 4

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Applying the distance formula, DE = a. Therefore, the missing information is: A. a.

Distance Formula for determining the distance between two points on a coordinate plane is given as: [tex]d = \sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex].

In the proof given, applying the distance formula to find DE, we have:

DE = √[(a + b -  b)² +  (c - c)²}

Simplifying this, we would have:

DE = √(a² + 0²) = √(a²)

DE = a

Therefore, the missing information in the proof is: A. a.

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Answer:

A. a

Step-by-step explanation:

got it right on edge23

1. There's so much wrong with the suggested solution that it's hard to pinpoint the exact error. The "logic" is inconsistent - why do the [tex]x[/tex] and constant term stay in the denominator but the [tex]x^2[/tex] term does not?

What should be done is factorization in the numerator and denominator:

[tex]x^2 + 2x - 8 = (x + 4) (x - 2)[/tex]

[tex]x^2 + 6x - 16 = (x + 8) (x - 2)[/tex]

Then in the quotient, the factors of [tex]x-2[/tex] cancel so that

[tex]\dfrac{x^2+2x-8}{x^2+6x-16} = \dfrac{(x+4)(x-2)}{(x+8)(x-2)} = \boxed{\dfrac{x+4}{x+8}}[/tex]

2. Use the same strategy: factorize everything everything you can, then cancel anything you can.

[tex]x^2 - 9 = (x-3) (x+3)[/tex]

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

[tex]x^2+x-12 = (x+4)(x-3)[/tex]

[tex]x^2+6x+8 = (x+4)(x+2)[/tex]

Then using the algebraic properties of multiplication/division, we have

[tex]\dfrac{x^2-9}{x^2+x-2} \div \dfrac{x^2+x-12}{x^2+6x+8} = \dfrac{x^2-9}{x^2+x-2} \times \dfrac{x^2+6x+8}{x^2+x-12} \\\\ ~~~~~~~~= \dfrac{(x-3)(x+3)(x+4)(x+2)}{(x+2)(x-1)(x+4)(x-3)} \\\\ ~~~~~~~~= \boxed{\dfrac{x+3}{x-1}}[/tex]

Answer:

Step-by-step explanation:

Note : I am assuming that the question is asking for all no. of total pens.

If 5 red pens were 25% of the total quantity, we can say that 1/4th of the pens were red.

If 5 pens = 1/4, we multiply 5 * 4 to find the total quantity. 5*4 = 20

So, Ms. Sullivan bought 20 pens.

Hope this helps!

Answer:

all real numbers or [tex](-\infty, \infty)[/tex]

Step-by-step explanation:

since both f(x) and g(x) are polynomials, neither of them have restrictions on their domains. Since they can be defined for all real numbers. It's not like the square root which has a domain of (0, infinity), or log x which is defined only from (0, infinity). So adding these two polynomials would result in a domain of all real numbers.

The first angle is 33.8° and second angle is 56.2°.

If the sum of the two angles is equal to the measurement of a right angle then the pair of angles is said to be complementary angles.

Complementary angles are the angles whose sum makes 90⁰.

Let's say our first angle is x:

x = first angle

According to the question,

The other angle is 22.4° more than the complementary angle.

Therefore, 22.4° will be added to the other angle.

first angle  = x

second angle = x + 22.4°

Since, complementary angle is equal to the sum of the two angles to be 90°.

∴ x + x + 22.4°  = 90°

    2x = 90 ° - 22.4°

    2x = 67.6°

     x = 67.6° / 2

     x = 33.8°

Thus, the first angle is 33.8° and second angle is 56.2°.

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The cat will be waiting and meowing at his bowl for 18.3 seconds.

The time it takes the cat to reach the bowl = 3.7 seconds (17/10 + 2)

The time it takes the woman to reach the bowl = 17 seconds (17/1)

The total time it takes the woman to put the food = 22 seconds (17 + 3 + 2)

Waiting time = 18.3 seconds (22 - 3.7)

Distance to the cabinet = 12 meters

Distance to the bowl = 5 meters

Total distance to be covered = 17 meters

Speed of the cat = 10 meters/s

Speed of the woman = 1 meter/s

Thus, since the time it takes is dependent on the speed of both, the cat will be waiting and meowing at his bowl for 18.3 seconds.

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The two general approaches are qualitative and quantitative.

Forecasting is a technique that uses past data as inputs to make future predictions by determining the direction of trends in the future.

It is an estimation methodology that uses judgment, other than numerical analysis. This type of forecasting depends upon the knowledge of most experienced employees and consultants to provide predictions for future outcomes.

It is a data-based math process that teams use to understand performance and predict future based revenue on the data and the patterns. Forecasting results gives businesses the ability to make informed decisions on strategies and processes to ensure continuous success

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The equation 3x² - 48x + 6856 represents the area of the gym and track together in terms of width.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

We have:

A rectangular building for a gym is three times as long as it is wide. Just inside the walls of the building, there is a 6ft rectangular track along the walls of the gym and has an area of 7000ft²

Let x be the width of the rectangle.

As the area of track along the walls of the gym is 7000ft²

(x - 12)(3x - 12) = 7000

After simplifying:

3x² - 48x + 6856 = 0

Thus, the equation 3x² - 48x + 6856 represents the area of the gym and track together in terms of width.

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Answer:

A and C

Step-by-step explanation:

multiplying the value by a fraction < 1 will give a value less than the original value.

multiplying the value by an integer greater than 1 will give a value greater than or equal to the original value

A and C have 6,766 multiplied by a fraction < 1 , then

A and C have a value less than 6,766

Answer: A and C

Step-by-step explanation: Every time you multiply a fraction by a whole number, you get less than the whole number

The toroid formed by rotating the rectangular figure gives;

a. A toroid

b. 374•π

c. 400•π

d. The surface area will be 4 times the initial surface area

The volume will be 8 times the initial volume

Taking the distance from the y-axis as 8

Width of the rectangle; 2.5

Length; 6

We have;

a. The solid of revolution is a toroid, having sharp corner edges

b. The surface area is found using the surface area of a hollow cylinder as follows;

Outer radius = 8 + 6 = 14

Inside radius = 8

Width = 2.5

Outer area = 2• π × 14 × 2.5 = 70•π

Inner area = 2• π × 8 × 2.5 = 40•π

[tex]{\pi \cdot 14 }^{2} - {\pi \cdot 8 }^{2} = 132 \cdot\pi[/tex]

The surface area of the figure is therefore;

c. The volume of the solid of revolution is found as follows;

[tex]{\pi \cdot 14 }^{2} \times 2.5 - {\pi \cdot 8 }^{2} \times 2.5= 400 \cdot \pi[/tex]

e. When the dimensions are doubled, we have;

The linear scale factor = 2

The area scale factor = 2^2 = 4

Therefore;

The volume scale factor = 2^3 = 8

The volume of the solid following the enlargement, is therefore;

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Answer:

-2

Step-by-step explanation:

It is to be noted that the flow rate is 50mL/h for the first instance, and;

100mL/h for the second instance.

Flow rate (Fr) is computed with the following formula:
Fr (mL/h) = Volume (mL)/ Time (Hours)

Time = 1 hour

Volume = 50 mL

It is to be noted that we don't need 500mg because it is already infused into the 50mL solution) hence,

Hourly flow rate = unknown

To compute for Flow Rate (Fr)

Recall that:

Fr (mL/h) = Volume (mL)/ Time (Hours)

Inserting the values we have
Fr = 50/1

Fr = 50mL/h

We have been given the following:
Time = 0.5 hours (30 minutes = 0.5 hours)

Volume = 50mL

It is to be noted that we don't need 500mg because it is already infused into the 50mL solution) hence

Fr = 50/0.5

Fr = 100 mL/h

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The probability that a customer spends 10+ hours or have below $40,000 is 0.6034

Let A represent spending 10+ hours, and B represent having below $40,000

The probability is then calculated using:

P(A or B) = P(A) + P(B) = P(A and B)

This gives

P(A or B)= (476 + 621 - 131)/1601

Evaluate the sum and difference

P(A or B)= 966/1601

Divide

P(A or B)= 0.6034

Hence, the probability is 0.6034

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Answer:

C

Step-by-step explanation:

Given y = amount of money spend for the long distance plan per month

and x = minutes used each month

Note these 2 plans are in per month basis.

Plan A: Flat $5 + $0.99 Per min used (variable cost)

transform into an equation:

y = 0.99x + 5

Plan B: Flat $10 + $0.79 per min used (variable cost)

transform into equation:

y = 0.79x + 10

Put these 2 equations together, will give you the answer as C.

The nearest tenth of how fast a rover will hit Mars' surface after a bounce of 15 ft in height is 20.7ft/s.

From the question:

Mars: F(x) = 2/3[tex]\sqrt{64x}[/tex]

Therefore, If x = 15

Then:

f (15) =  2/3 [tex]\sqrt[8]{15}[/tex]

= 16/3[tex]\sqrt{15}[/tex]

= 20.7ft/s

Hence, The nearest tenth of how fast a rover will hit Mars' surface after a bounce of 15 ft in height is 20.7ft/s.

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The number of cube that can be packed in the rectangular prism is 30 cubes

Volume of the rectangular prism in terms of small cube and unit cube = 30(1 / 8) ft³

volume of rectangular prism = lwh

where

Therefore,

volume of rectangular prism = 3 / 2 × 1 × 5 / 2  = 15 / 4 ft³

volume of cube = 1 / 2 × 1 / 2 × 1 / 2  = 1 / 8 ft³

number of cube that can be packed in the rectangular prism = 15 / 4 × 8 =  30 cubes

Volume of the rectangular prism in terms of small cube and unit cube = 30(1 / 8) ft³

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Using the above conditions ; If m ∠LOM = m ∠JKI,  if m ∠MON = m ∠IKH it is proved below that m ∠LON = m ∠HKJ as are congruent angles.

An angle is known to be Congruent if its angles do have equal measure."

Note that question, In the said figure of the angles (image attached),

m ∠LOM = m ∠JKI  (congruent angles)              taken as 1      

m ∠MON = m ∠IKH  (congruent angles)             taken as 2  

The one should sum up both the side angle  of m ∠MON in (1) we obtain;

m ∠LOM + m ∠MON = m ∠JKI + m ∠MON

Then one should replace angle  m ∠MON = m ∠IKH from (eqn. 2)  on right hand side and then it will be:

m ∠LOM + m ∠MON = m ∠JKI + m ∠IKH      taken as (3)

Then:

m ∠LOM + m ∠MON = m ∠LON  ( M is said to be the interior point of ∠LON)    taken as (4)

Since m ∠JKI + m ∠IKH = m ∠HKJ  ( I is said to be the interior point of ∠HKJ)            taken as number (5)

Using Number (3) , (4) and (5)  in the image attached, we obtained:

m ∠LON = m ∠HKJ  (Congruent angles)

Therefore, Using the above conditions ; If m ∠LOM = m ∠JKI,  if m ∠MON = m ∠IKH it is proved below that m ∠LON = m ∠HKJ as are congruent angles.

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Consider repeating the study using a larger sample.

Too small a sample may prevent the findings from being extrapolated, whereas too huge a sample may additionally increase the detection of differences, emphasizing statistical variations that are not clinically relevant.

Selecting the proper sample length will increase the chance of detecting an impact, and ensures that the look is both ethical and value-powerful. Repeated measures designs are widely used due to the fact they have got blessings over pass-sectional designs.

Larger sample sizes provide extra accurate mean values, perceive outliers that would skew the information in a smaller pattern and provide a smaller margin of blunders.

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