6. Using the discriminant, determine the value of k that will give 1 solution (i.e. discriminant equals zero) y = kx²-4x + 4 ​

Answer:

The balance after 37 years is $3869.99

Step-by-step explanation:

Given:

The Amount (A),

A = P (1 + [tex]\frac{R}{100n}[/tex][tex])^{nt}[/tex]        if compound n times per year

Amount (A) at 37 years,

A = ($2,520) (1 + [tex]\frac{1.16}{100(12)}[/tex][tex])^{12 x 37}[/tex]

A = ($2,520) (1 + [tex]\frac{1.16}{1,200}[/tex][tex])^{444}[/tex]

A = ($2,520) (1.00096667 [tex])^{444}[/tex]

A = ($2,520) (1.5357)

A = $3869.9944

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Answer:

29/60

Step-by-step explanation:

probability of playing is 290/600 which when simplified is29/60

The order of the graphs from largest to lowest correlation coefficients is:

Graph D, Graph A, graph C, graph B.

The correlation coefficient between two variables is a coefficient that tells us "how much" these variables relate.

So, in the case for linear correlation, as "more linear" the data appears to be, a large correlation is between the two variables.

With that in mind, we conclude that the order of the graphs (going for larger correlation coefficient to smaller correlation coefficient) is:

Graph D, Graph A, graph C, graph B.

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Answer:

need more info

Step-by-step explanation:

what I can tell you is that when you change all the x's in the equation to 6s, both sides of the equation will equal eachother.

The value of angle ∠DEC  = 60 degree.

The complete question is

In the given the figure above, m∠BAC = 64° and m∠CBA = 56°.

Part I: Find the m∠DEC.

Part II: Explain the steps you took to arrive at your answer. Make sure to justify your answer by identifying any theorems, postulates, or definitions used.

A triangle is a polygon with three sides and three vertices and three angles.

As it is given that

AB || CD

Let BC be the transversal , then

∠CBA = ∠DCB (alternate opposite angles)

∠DCB = 56 degree

As the sum of opposite interior angle sis equal to exterior angle therefore ∠ ECB = 120 degree

∠DCE = 120-56 = 64 degree

BC || DE

∠EDC = ∠DCB = 56 degree (alternate opposite angles)

Sum of all the interior angles of a triangle is equal to 180 degree

56 +64+∠DEC = 180

∠DEC  = 60 degree.

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Answer:

x<7

Step-by-step explanation:

Consider the number x (as mentioned in the question). Now carefully pay attention to the given condition

⇒"The sum of a number and 3 is less than 10"

Remember the notation of  the term "less than" in mathematical context is indicated by "<" sign. Hence our inequality is

⇒ x+3<10

adding or subtracting any number from the both sides of an inequality DOESN'T change its direction. Thus, if we cancel out 3 from both sides it won't swap the inequality. Therefore

⇒ x+3-3<10-3

⇒ [tex]x<7[/tex]

In terms of  interval notation

[tex]\implies x\in( -\infty,7)[/tex]

In conclusion

The answer is D) [tex]x < 7[/tex]

Let the number be x

The sum of number and 3

Is less than 10

Lets solve it

Hence

Option D is correct

Answer:

Step-by-step explanation:

Several trig identities are involved in the proof of this. This is the order in which they are used.

Starting with the left side, we can transform it into the right side.

  [tex]2\cos(2x)=2(\cos^2(x)-\sin^2(x)) = 2(\cos^2(x)-(1-\cos^2(x)))\\\\=2(2\cos^2(x)-1)=2\left(\dfrac{2}{\sec^2(x)}-\dfrac{\sec^2(x)}{\sec^2(x)}\right)\\\\=\boxed{\dfrac{4-2\sec^2(x)}{\sec^2(x)}}[/tex]

Answer:

D.

because 2 times 120 reduced.

Answer:

-4 x³+2x²-5x+3x²

combine like terms

-4x³ +5x²-5x

common factors

-1(4x³-5x²+5x)

find one factors

Ans: -x (4x²-5x+5)

Answer:

Step-by-step explanationp :

ph =lo 4

Answer: B(1, 3) and D(1, −2)

Step-by-step explanation:

The distance from A to C is 5, meaning we need the length to be 4.

If they lie to the right, we need to add 4 to the x coordinates, so the x coordinates should be 1, and the y coordinates should be 3 and -2.

The locations of B and D are given by (A) B(1,3) and D(1,-2).

The area of rectangle is given by the product of the length and width of that rectangle.

Area = Length*Width

Distance between two points (a,b) and (c,d) is given by,

[tex]d=\sqrt{(c-a)^2+(d-b)^2}[/tex]

Here in the given question it is mentioned that AC forms width of a rectangle and A is at (-3,3) and C is at (-3,-2)

Now the width is [tex]=\sqrt{(-3-(-3))^2+(-2-3)^2}=\sqrt{0^2+(-5)^2}=\sqrt{25}=5[/tex] unit.

Also it is given that, the area of the rectangle is 20 square units.

So the length is = 20/5 = 4 units

B and D lie to the right of points A and C respectively.

We have to go 4 units right to the A to find B and 4 units right to C to find D.

A is at (-3,3)

then B is at (-3+4,3) = (1,3)

C is at (-3,-2)

So D is at (-3+4,-2) = (1,-2)

Hence correct option is (A) B(1,3) and D(1,-2)

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The slope of the linear function is 3 and the y-intercept is -3 if the linear function contains the following points: (0,-3) and (6,15)

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have:

A linear function contains the following points: (0,-3) and (6,15)

The slope:

[tex]\rm m =\dfrac{15-(-3)}{6-0}[/tex]

m = 18/6

m = 3

The equation of a line:

y = mx + c

Plug x = 0, y = -3

-3 = c

Thus, the slope of the linear function is 3 and the y-intercept is -3 if the linear function contains the following points: (0,-3) and (6,15)

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The marginal cost when x = 25 and when x = 100 are $0.1 and $0.05 respectively.

A marginal production cost is a derivative of a cost function. From the information given, the total cost is:

The marginal production cost can be expressed as:

[tex]\mathbf{C'(x) = \dfrac{d}{dx}(\sqrt{x})}[/tex]

[tex]\mathbf{C'(x) = \dfrac{1}{2\sqrt{x}}}[/tex]

However, when the cost is 25, the marginal production is:

[tex]\mathbf{C'(25) = \dfrac{1}{2\sqrt{25} }}[/tex]

[tex]\mathbf{C'(25) = \dfrac{1}{2\times5}}[/tex]

[tex]\mathbf{C'(25) = \dfrac{1}{10}}[/tex]

C' (25) = $0.1

Also, when the cost is 100, the marginal production is:

[tex]\mathbf{C'(100) = \dfrac{1}{2\sqrt{100} }}[/tex]

[tex]\mathbf{C'(100) = \dfrac{1}{2\times10}}[/tex]

[tex]\mathbf{C'(100) = \dfrac{1}{20}}[/tex]

C' (100) = $0.05

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Answer:

9a + 18

Step-by-step explanation:

so the first step is to evaluate the value of f(2).

[tex]f(2) = 9(2)^2-7\\f(2)=9(4)-7\\f(2)=36-7\\f(2)=29[/tex]

Now that we have this value we can use the slope formula (y2 - y1) / (x2 - x1) where y2 is f(a), y1 is 29, x2 is a, and x1 is 2

[tex]\frac{f(a)-29}{a-2}\\\\\frac{(9a^2-7)-29}{a-2}\\\frac{9a^2-36}{a-2}[/tex]

Now from here we can use long division to simplify it further

[tex]9a^2/a = 9a\\9a(a-2)=9a^2-18a\\(9a^2-36)-(9a^2-18a)\\18a-36\\\\18a/a=18\\18(a-2)=18a-36\\(18a-36)-(18a-36)\\0\\\\9a+18[/tex]

Answer:

it should be option A

and in option there should be "x" instead of "*"

Equation of circle is,

⇒ (x + 1)² + (y - 2)² = 9

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The circle below is centered at the point (-1, 2) and has a radius of length 3.

Now, We get;

The equation of circle is,

⇒ (x - (- 1))² + (y- 2)² = 3²

⇒ (x + 1)² + (y - 2)² = 9

Thus, Equation of circle is,

⇒ (x + 1)² + (y - 2)² = 9

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The student did not make any mistake, the solution is correct. Then the correct option is A.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

A student perform the following steps to find the solution of the equation x² – 2x – 15 = 0.

The factor of the equation will be

Step 1 :  x² – 2x – 15 = (x – 5)(x + 3)

Step 2 : (x – 5) = 0 and (x + 3) = 0

Step 3 : x = 5 and – 3

The student did not make any mistake, the solution is correct.

Then the correct option is A.

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

Explanation:

Use the rational root theorem to determine this list of possible rational roots: 1, -1, 1/2, -1/2

Plug each possible root one at a time into the original expression given. If the simplified result is 0, then that possible root is an actual root.

If we tried say a = -1, then,

2a³-a²+a-2​ = 2(-1)³-(-1)²+(-1)-2​ = -6

The result is not zero, so a = -1 is not an actual root.

But if we tried say a = 1, then,

2a³-a²+a-2​ = 2(1)³-1²+1-2​ = 0

We get 0 so a = 1 is an actual root. I'll let you try the other values, but you should find that a = 1 is the only rational root.

Since a = 1 is a root, this makes (a-1) to be a factor.

From here, use either synthetic or polynomial long division to determine the other factor. Refer to the diagram below for each method.

Regardless of which method you pick, the quotient is 2a² + a + 2 which is the other factor needed. The remainder of 0 tells us we have (a-1) as a factor. For more information, check out the remainder theorem.

Answer:

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

A relation is a function if each value of x maps onto no more than one value of y.

I'm assuming you meant to write y = 3x-4

We know that the y-intercept of the given line is (0,-4), so we need to find the equation of the line passing through (-2,5) and (0,-4).

The slope is

[tex]\frac{-4-5}{0-(-2)}=-\frac{9}{2}[/tex]

So, this means the equation is [tex]\boxed{y=-\frac{9}{2}x-4}[/tex]

Using translation concepts, the correct statement is given by:

If function f was translated down 4 units, the f(x) values would be subtracted by 4. A point in the table for the transformed function would be (1,9).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

A translation down 4 units means that the output values are subtracted by 4, hence the table would be given by:

x    1  2  3   4    5

f(x) 9 15 33 87 249

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Answer:

The CORRECT answer is:

1. f(x)

2. decreased by 4

3. (4, 87)

Step-by-step explanation:

Took the test

Answer:

the first,second,forth and fifth.

Step-by-step explanation:

I got it off of edg.

Here you go! please make sure you read it all too understand it, and make sure you try work before asking for help :D Have a awesome day/night

Answer:735

Step-by-step explanation:I was hoping you’d have another. Dv/dt=d/dt((7+5t)^3)=3x5x((7+5t)^2)=15x49. Does this work?

Answer:

2.6 hours

Step-by-step explanation:

Let t be the time that the trains meet.

[tex]90t = 416 - 70t[/tex]

[tex]160t = 416[/tex]

[tex]t = 2.6[/tex]

Step-by-step explanation:

option 2 is correct

here the question ask for value of X

to find it we multiple the matrix X with the given matrix in question and equate the answer.

The coordinates of the turning point of the graph of the quadratic equation is given by: (-6.25, -75.13).

A quadratic equation is modeled by:

[tex]y = ax^2 + bx + c[/tex]

The vertex is given by:

[tex](x_v, y_v)[/tex]

In which:

In this problem, the function is given by:

y = 2x² + 25x + 3.

Hence the coefficients are a = 2, b = 25, c = 3, then the coordinates of the vertex are given as follows:

The coordinates of the turning point of the graph of the quadratic equation is given by: (-6.25, -75.13).

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Answer:

6.25, -75.13

Step-by-step explanation:

it just is

The only true statement is A:

"The data show a negative linear relationship."

On the graph, we can see how the car's vale decreases almost linearly with the age of the car.

Where the response variable would be the one on the y-axis, which is the car's value.

For that linear behavior, we know that there is a correlation coefficient different than zero. So options B, C, and D are false.

Finally, we already saw the linear behavior (decreasing, so the slope is negative). Then we conclude that the only true statement is A.

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The system of the linear inequality that fulfill the condition of the graph will be y ≥ 2x – 1 and y ≤ 1/3 x + 1. Then the correct option is A.

The complete question is attached below.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The system of the linear inequality that fulfill the condition of the graph will be

y ≥ 2x – 1

y ≤ 1/3 x + 1

Then the correct option is A.

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Answer: 30 and 7

Step-by-step explanation: 30 plus 7 is 37, 30 times 7 is 210