Find the values of k for which the quadratic equation 2x^2 − (k + 2)x + k = 0 has real and equal roots.

Answer:

-2i/15 and 2i/15

Step-by-step explanation:

Difference of Squares:

(15x+2i)(15x-2i)

Answers: -2i/15 and 2i/15

Answer:

A) 0.9(sin50)

Step-by-step explanation:

Since this is a right triangle, we can use

sin a = opposite side/ hypotenuse

sin 50 = x /.9

Multiply each side by .9

.9 * sin 50 = x/.9 * .9

.9 (sin 50) = x

A football quarterback enjoys practicing his long passes over 40 yards. He misses the first pass 40% of the time. When he misses on the first pass, he misses the second pass 20% of the time. What is the probability of missing two passes in a row?

30%

Probability of missing two passes in a row is 0.08.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given

Event E = A football player misses twice in a row.

P(E) = ?

Event X = Football player misses the first pass

P(X) = 0.4

Event Y = Football player misses just after he first miss

P(Y) = 0.2

Both the events are exclusive so the probability of occurring of these two events can be calculated by the formula:

P(E) = P(X).P(Y)

P(E) = 0.4*0.2

P(E) = 0.08

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Answer:

Step-by-step explanation:

The unknown [tex]x[/tex] and the numbers are mixed in the given equation. However, in the desired equation, the left-hand side contains only the unknown while the right-hand side contains only numbers.

Start with the given equation. That's statement 1.

The question chooses to move the number [tex]-2[/tex] from the right-hand side of the equation to the left-hand side in statement 2. This change can be done by adding [tex]2[/tex] (the opposite of [tex]-2[/tex]) to both sides of the equation.  

In statement 3, The question moves the term with the unknown [tex]4x[/tex] from the left-hand side of the equation to the right-hand side. This change can be done by adding [tex]-4x[/tex] (the opposite of [tex]4x[/tex]) to both sides of the equation.

The coefficient of the unknown [tex]x[/tex] in statement 3 is [tex]2[/tex]. In statement 4, the question turns this coefficient into [tex]1[/tex]. This change can be done by dividing both sides by the coefficient of [tex]x[/tex]. Keep in mind that multiplying both sides with the reciprocal of that coefficient, [tex]1/2[/tex], will achieve the same effect.

By the symmetric property of equality, [tex]a = b[/tex] if and only if [tex]b = a[/tex]. In other words, if [tex]3/2 = x[/tex] is true, [tex]x = 3/2[/tex] must also be true. That leads to statement 5.

Answer:

I believe it's a scalene triangle

D. Scalene

Hope this helps

Step-by-step explanation:

Scale = No equal sides and No equal angles

[tex](f-g)(x)=3x+10-(4x-2)=3x+10-4x+2=-x+12[/tex]

Answer:

A.

Step-by-step explanation:

The slope would be -2/3 and the y-intercept is -6

For this case we must indicate the graph of the following equation:

[tex]-6x-9y = 54[/tex]

Adding 6x to both sides we have:

[tex]-9y = 54 + 6x[/tex]

Dividing between -9 on both sides:

[tex]y = \frac {54} {-9} + \frac{6x} {-9}\\y = -6 - \frac {2} {3} x[/tex]

For an equation of the form[tex]y = mx + b[/tex], the slope is given by "m" and the point of intersection with the y axis is "b".

In this case we have that[tex]b = -6[/tex] and[tex]m = -\frac {2} {3}[/tex]. The slope is negative. So, the corresponding graph is option A

Answer:

Option A

In geometry, you can use deductive rules to prove conjectures

A coordinate geometry is a branch of geometry where the position of the points on the plane is defined with the help of an ordered pair of numbers also known as coordinates.

Deductive reasoning is used in geometry to start with a set of given premises or axioms, and then use logical reasoning and previously established theorems to draw conclusions or prove conjectures.

The main use of deductive rules in geometry is to prove conjectures.

A conjecture is considered proven only when it has been shown that it is logically impossible for it to be false.

Hence, in geometry, you can use deductive rules to Prove conjectures

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Answer:

no

Step-by-step explanation:

There is no consistent scale factor.

Answer:

No

Step-by-step explanation:

For triangles to be similar there must be a proportion between their measurements.

That is, for example if from one triangle to another one side doubled, all other sides must also double.

The triangle side on the left sides measure 1.5, 1 and 2.

In the right triangle the sides measure 0.5, 1 and 1.5

There is no proportion factor that serves to convert all the measures of the first triangle to those of the second triangle.

So the triangles are not similar.

Answer:

1045 females

Step-by-step explanation:

First, lets calculate how many males there are.

52.5% of 2200 = 1155

Then, calculate the difference between the males and the total.

2200-1155=1045

Have a wonderful day!

There are 1045 female students in the school

The proportion of male students is given as:

Male proportion = 52.5%

This means that the female proportion is:

Female = 100% - 52.5%

Female = 47.5%

The number of  female students is then calculated as:

Female = 47.5% * 2200

Evaluate

Female = 1045

Hence, there are 1045 female students in the school

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Answer:

3181 yards.

Step-by-step explanation:

All the given information can be used to draw a simple diagram. The diagram shows a triangle which is formed by the ships. There are two angles given and one side is given. Therefore, the sine rule must be used to solve the question. The sine rule can be written as:

sin V / v = sin G / g.

It can be observed that the angle V is unknown, however, it can be calculated very easily. Simply use the law of triangle in which all the 3 angles sum up to 180 degrees. So V = 180 degrees - 44 degrees - 36 degrees = 100 degrees. So plugging in v = 4510 yards, V = 100 degrees, G = 44 degrees, and g = x yards into the sine rule gives:

sin 100 / 4510 = sin 44 / x.

Cross multiplying gives:

x*sin 100 = 4510*sin 44

Making x the subject gives:

x = (4510*sin 44)/sin 100.

x = 3181 yards (to the nearest yard).

Therefore, Norman and Voyager are 3181 yards apart from each other!!!

Answer:

[tex]f(x)=\frac{3}{2}x-2[/tex]

Step-by-step explanation:

step 1

Find the slope m

we have

(-2,-5) and (4,4)

The slope is equal to

[tex]m=\frac{4+5}{4+2}[/tex]

[tex]m=\frac{9}{6}[/tex]

simplify

[tex]m=\frac{3}{2}[/tex]

step 2

Find the equation of the line into slope point form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=\frac{3}{2}[/tex]

[tex](4,4)[/tex]

substitute

[tex]y-4=\frac{3}{2}(x-4)[/tex]

step 3

Convert to slope intercept form

[tex]y-4=\frac{3}{2}(x-4)[/tex]

[tex]y=\frac{3}{2}x-6+4[/tex]

[tex]y=\frac{3}{2}x-2[/tex]

Convert to function notation

[tex]f(x)=\frac{3}{2}x-2[/tex]

Answer:

Option A (0,a)

Step-by-step explanation:

we know that

[tex]f(x)=a(b^{x})[/tex]

Is a exponential function

where

a is the initial value

b is the base

Remember that

The initial value is the value of the function when the value of x is equal to zero (y-intercept)

therefore

For x=0

[tex]f(0)=a(b^{0})[/tex]

[tex]f(0)=a(1)=a[/tex]

The y-intercept is the point (0,a)

Answer:

(0, a)

Step-by-step explanation:

Final answer:

The conditional probability of drawing a white ball on the second draw after a blue ball has been drawn on the first draw from a bag of balls without replacement is 2/7.

Explanation:

The question asks for the probability of drawing a white ball on the second draw, given that a blue ball has been drawn on the first draw (P(B|A)) from a bag containing 4 blue balls, 7 yellow balls, and 4 white balls, without replacement.

Firstly, we calculate the total number of balls in the bag: 4 blue + 7 yellow + 4 white = 15 balls.

For event A (drawing a blue ball first), there are 4 ways this can happen out of 15 total possibilities, so the probability of A is 4/15. After a blue ball is drawn, there are now 14 balls left in the bag for the second draw.

Since event B is drawing a white ball as the second ball, given that a blue ball has already been drawn on the first draw, there are still 4 white balls left in the bag after event A has occurred. Therefore, the probability of B given A is 4/14, which simplifies to 2/7.

Thus, P(B|A) = 2/7.

Answer:

Option B is correct.

Step-by-step explanation:

To check if the lines are parallel or perpendicular, we need to find the slope of lines AB and CD

A=(-8,1), B= (-2,4), C= (-3, -1), and D= (-6,5)

Slope of AB = y₂-y₁/x₂-x₁

Slope of AB = 4-1/-2-(-8)

Slope of AB = 3/-2+8

Slope of AB = 3/6

Slope of AB = 1/2

Slope of CD = y₂-y₁/x₂-x₁

Slope of CD = 5+1/-6-(-3)

Slope of CD = 6/-6+3

Slope of CD = 6/-3

Slope of CD = -2

Lines are parallel if Slope of AB = Slope of CD

Lines are perpendicular if Slope of Ab = -1/Slope of CD

So, Slope of AB = 1/2

Slope of CD = -2

So, LINE AB AND LINE CD ARE PERPENDICULAR

Option B is correct.

Answer:

$17.85

Step-by-step explanation:

Let the dollar amount per shirt be represented by s.

Let the dollar amount per pants be represented by p.

You have the following system:

3s+2p=104.81

2s+1p=61.33

If I multiply the bottom equation by -2, I can set the system up for elimination since the equations are already and the same form and I will have 2p and -2p in the same column there.  2p+(-2p)=0

Multiplying equation 2 by -2:

3s+2p=104.81

-4s-2p=-122.66

-----------------------Add the equations:

-1s      =-17.85

Multiply both sides by -1:

s=17.85

So one shirt cost $17.85

Answer:

x = 20

Step-by-step explanation:

The converse of the same side exterior angles theorem states that when two same side exterior angles are supplementary, the two lines they are on are parallel.

So that means that 5x + 9 and 3x + 11 are supplementary.

Therefore, 5x + 9 + 3x + 11 = 180.

Add like terms: 8x + 20 = 180

Subtract: 8x = 160

Divide: x = 20

Answer:

*To be honest, we have a bunch of ways to find x, but I'm only going to use one.

So in order for A║B, we need the outer angle of these two lines but on the opposite sides to be equal, which means:

   5x + 9 = 180 - (3x + 11)

⇔ 5x + 3x = 180 - 9 - 11

⇔ 8x         = 160

⇔ x            = 160/8 = 20

So x is equal to 20.

Answer:

B. f(x) =-150+1500

Step-by-step explanation:

Let x represents the number of months and y represents the savings account balance ( in dollars )

Thus, table would be,

x            0              2              4              6

y        1,500       1,200       900          600,

Let the linear function that represents the above table is,

y = mx + c

By the table,

1500 = m(0) + c ⇒ c = 1500,

Again by the table,

1200 = m(2) + c

1200 = 2m + 1500

-300 = 2m ⇒ m = -150

The function would be,

y = -150x +1500

Since, 900 = -150(4) + 1500

600 = -150(6) + 1500

The whole table satisfy the equation y = -150x +1500,

Hence, the linear function that models the given table is,

y = -150x +1500

Option 'B' is correct.

Answer:

b

Step-by-step explanation:

Answer:

The approximate solution is: x = -2.29; y = 0.46

Step-by-step explanation:

8x - 10y = -23

9x + 10y =-16

Since you have -10y in one equation and 10y in the other equation, add the equations to eliminate y and solve for x.

17x = -39

x = -39/17

Now substitute -39/17 for x in the first equation, and solve for y.

8(-39/17) - 10y = -23

-312/17 - 10y = -391/17

-10y = -79/17

y = 79/170

The exact solution is x = -39/17; y = 79/170

The approximate solution is: x = -2.29; y = 0.46

Step-by-step explanation:

Any line passing through (-3,7) and (6,4) is,

y-y1=(y2-y1) (x-x1)

(x2-x1)

y-7 = (4-7) (x+3)

(6+3)

y-7 = (-3/9)(x+3)

y-7= (-1/3)(x+3)

3y-21=-x-3

x+3y-21+3=0

x+3y-18=0

Which h is the required line.

Answer:

A

Step-by-step explanation:

=====================================

How I got that answer:

A sequence is geometric if you are able to divide any term over its prior one and get the same result each time. Note with something like choice A we have...

term2/term1 = 13/6 = 2.17 (approx) and term3/term2 = 19/13 = 1.46

the results 2.17 and 1.46 are not the same, so we can rule out choice A

---------

Choice B however, we have...

term2/term1 = 3/(-3) = -1

term3/term2 = -3/3 = -1

term4/term3 = 3/(-3) = -1

each time we get -1, so this is the common ratio. We can multiply each term by the common ratio -1 to get the next term, for instance,

term2 = (common ratio)*(term1) = -1*(-3) = 3

term3 = (common ratio)*(term2) = -1*3 = -3

and so on. This proves that sequence B is geometric. Sequences C and D are not geometric for similar reasoning to choice A.

The expression 4h² + g has no common factors or recognizable factoring patterns, and is thus already in its simplest form; it cannot be factored further.

To factor completely the expression 4h² + g, we would look for common factors or recognizable patterns like the difference of squares, perfect square trinomials, or other factoring techniques. However, since 4h² and g have no common factor and the expression is not a difference or sum of cubes, or any other known factoring pattern, it cannot be factored further (assuming g is a constant). In other factoring scenarios, one might look for techniques like grouping, but that's not applicable here either. Therefore, the expression 4h² + g is already in its simplest, factored form as there are no common factors between the terms.

Answer:

[1, 1]

Step-by-step explanation:

When you plug in these coordinates, you will see that 4 + 2 = 6.

I am joyous to assist you anytime.

Answer:

7.5 mph.

Step-by-step explanation:

Speed downstream = d / 3 = 30 + x    where d = the distance , x =speed of the stream.

Speed upstream = d  / 5 = 30 - x.

30 + x = d/3

30 - x = d/5

Adding the 2 equations

60 = d/3 + d/5

8/15 d = 60

d = 60 * 15 / 8 =  112.5 miles.

Now calculate x , the speed of the stream:

112.5 / 3 = 30 + x

x = 112.5 / 3 - 30

= 7.5 mph.

Answer:

0.0002

Step-by-step explanation:

0.00021 is a 2 significant figure .after the decimal point the zero can be counted as a significant figure or not ,it depends

Answer:

0.0002.

Step-by-step explanation:

The first significant figure is 2 and since 1 is the second significant figure  ( 1 is < 5) the 2  is retained.

Answer:

[tex]\large\boxed{y-3=\dfrac{2}{3}(x-2)}[/tex]

Step-by-step explanation:

[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\===============================[/tex]

[tex]\text{The point-slope form of an equation of a line:}\\\\y-y_1=m(x-x_1)\\\\m-slope\\\\(x_1,\ y_1)-point\ on\ a\ line\\\\===============================[/tex]

[tex]\text{We have the equation of a line:}\ y-9=\dfrac{2}{3}(x+7)\to m_1=\dfrac{2}{3}.\\\\\text{A slope of parallel line:}\ m_2=m_1=\dfrac{2}{3}.\\\\\text{Put the value of the slope and the coordinates of the point (2, 3)}\\\text{to the equation of a line in point-slope form:}\\\\y-3=\dfrac{2}{3}(x-2)[/tex]

Answer:

The answer is y = -3/2x + 6

Step-by-step explanation:

Answer:

9/4

Step-by-step explanation:

x^2+3x

Take the coefficient of the x term, 3

Then divide by 2,  3/2

Then square it  (3/2) ^ = 9/4

This is what you need to add to complete the square

[tex]-x=-8\\x=8[/tex]

Answer:

x = 8

Step-by-step explanation:

The solution set of - x = -8 is x=8.

- x = -8 = x = 8

Answer:

f^-1(x) = 9(x+2)

Step-by-step explanation:

To find the inverse function, exchange x and y and then solve for y

y = 1/9 x -2

Exchange x and y

x = 1/9 y-2

Solve for y

Add 2 to each side

x+2 = 1/9 y-2+2

x+2 = 1/9y

Multiply each side by 9

9(x+2) = 9*1/9y

9(x+2) = y

The inverse function

f^-1(x) = 9(x+2)

Answer:

9x+18

Step-by-step explanation:

[tex]f^{-1}[/tex] means they want you to find the inverse function of y=1/9 x-2.

The inverse is just a swapping of x and y.

People tend to remake the y part the subject again because they want to write it as a function.

Let's start:

[tex]y=\frac{1}{9}x-2[/tex]

Swap x and y:

[tex]x=\frac{1}{9}y-2[/tex]

Now it's time to solve for y:

Add 2 on both sides:

[tex]x+2=\frac{1}{9}y[/tex]

Multiply both sides by 9:

[tex]9(x+2)=y[/tex]

Distribute:

[tex]9x+18=y[/tex]

So The inverse function is:

[tex]f^{-1}(x)=9x+18[/tex]

A piecewise function is a function that is defined by several different formulas depending on the input (x). In this case, the function f(x) is a horizontal line for 0 ≤ x ≤ 20. The equation for this function would be y = constant, for 0 ≤ x ≤ 20, where the constant value is defined by the height of the horizontal line on the graph.

To write the equation of the piecewise function that is represented by a graph, you need to identify the different segments of the function and write a mathematical expression that describes each segment. In your case, the function f(x) is a horizontal line and is only defined between x = 0 and x = 20 (both inclusive). So, if we let y = f(x) be the horizontal line, then for the domain 0 ≤ x ≤ 20, the piecewise function can be written as:

Note that the 'constant' value of y is defined by the height of the horizontal line on the graph. This specification assumes that there are no other pieces to the function outside the range of x = 0 to x = 20.

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