Use the discriminant to describe the roots of each equation. Then select the best description.
x2 - 4x + 4 = 0​

Answer:

There is only 1 plane that contains all 3 points.

Step-by-step explanation:

According to the three point postulate, three non-collinear points are in one plane. Therefore, your answer would be there is only 1 plane that contains all 3 points.

Let's analyze each statement regarding the three non-collinear points:
1. "The intersection of 2 planes would contain all 3 points."
This statement is false. The intersection of two planes in three-dimensional space is a line, and there is no guarantee that a line resulting from the intersection of two arbitrary planes will contain all three non-collinear points. In fact, the likelihood of this happening by chance is zero.
2. "They will be contained in the same line."
This statement is false as well. Since the points are non-collinear, by definition, they do not all lie on a single line. A line can only contain two of the points at a time, but not all three if they are non-collinear.
3. "There is only 1 plane that contains all 3 points."
This statement is true. Given any three non-collinear points in space, there is exactly one plane that contains all three. This is because any three points that are not on the same line can define a plane by being unique points in a two-dimensional subspace of three-dimensional space.
4. "Only one line can be drawn containing any 2 of the points."
This statement is true as well. For any two distinct points, there exists exactly one line that connects them. This is one of the fundamental principles of geometry: through any two points, there is exactly one straight line.
In summary, the third and fourth statements are true, while the first and second are false.

Answer:

x∈ (11, +∞)

x∈ (-∞, 7)

Step-by-step explanation:

6|x-9|>12 :Split into possible cases

6(x-9)>12, x-9≥0 : solve the inequalities

x>11, x≥9

x<7, x<9 : find the intersections

x∈ (11, +∞)

x∈ (-∞, 7)

Answer:

(8,10)

Step-by-step explanation:

If we reflect a point over the y-axis, the x becomes opposite while the y stays the same.

So the rule here is (a,b)->(-a,b) if we are reflecting over y-axis.

So if you reflect (-8,10) over the y-axis you get (8,10).

Answer:

C. There are infinitely many solutions.  

Step-by-step explanation:

3x – 6 < 3x + 13

Subtract 3x from each side

-6 < -13

This inequality is always true.

There are infinitely many solutions.

After simplifying the inequality, it becomes apparent that it holds true for all values of x. Therefore, there are infinitely many solutions to this inequality.

To solve the inequality 3x – 6 < 3x + 13, we need to isolate the variable x on one side. However, when we attempt to subtract 3x from both sides to move the terms involving x to one side, we are left with – 6 < 13 which is a true statement, but no longer contains the variable x. This means that the inequality holds true for all values of x. Therefore, the solution to the inequality is that there are infinitely many solutions. No matter what value of x you choose, the inequality will always be true.

Answer:

False

Step-by-step explanation:

It would be at -3,9.

Answer:

b = -9

Step-by-step explanation:

As we go from M(4, 3) to N(7, 12), x increases by 3 and y increases by 9.  Thus, the slope of the line segment connecting these two points is m = rise / run = m = 9/3, or just m = 3.

Subbing the coordinates of M into y = mx + b, we get:

3 = 3(4) + b, or 3 = 12 + b, so that b = -9.

Answer:

-9

Step-by-step explanation:

Answer:

please could you send graphics A,B,C. you just sent D.

Answer:

The angles do not have the same reference angle.  

Step-by-step explanation:

We can answer this question by referring to the unit circle.

The reference angle of 5π/6 is π/6, and the reference angle of 5π/3 is π/3.

B, C, and D are wrong. Tangent is negative in both quadrants

Tan(5pi/6) and tan(5pi/3) are both equal to -sqrt(3), so they are equal.

Tan is a trigonometric function that represents the ratio of the opposite side to the adjacent side of a right triangle. Tan(x) is equal to sin(x) / cos(x).

When we evaluate tan(5pi/6), we find that it is equal to -sqrt(3).

When we evaluate tan(5pi/3), we find that it is equal to -sqrt(3).

Therefore, both tan(5pi/6) and tan(5pi/3) are equal to -sqrt(3), so they are equal.

Answer:

-3

Step-by-step explanation:

-9+6

=6-9

=-3

Answer:

-3

Step-by-step explanation:

-9+6

- + = -

So this expression will be subtracted.

-9+6 = -3

The answer is negative because greater value has a negative sign....

The next step for the evaluation of the given expression is:

         [tex](3)(5)+(\dfrac{1}{3})(5)+(3)(\dfrac{1}{4})+(\dfrac{1}{3})(\dfrac{1}{4})[/tex]

We are given an arithmetic expression as follows:

      [tex](3+\dfrac{1}{3})(5)+(3+\dfracx{1}{3})(\dfrac{1}{4})[/tex]

Now, in order to solve the given arithmetic expression we need to use the distributive property.

i.e.

[tex](a+b)c=a\cdot c+b\cdot c[/tex]

Now, the expression in the next step is written as follows:

[tex](3+\dfrac{1}{3})(5)+(3+\dfracx{1}{3})(\dfrac{1}{4})=(3)(5)+(\dfrac{1}{3})(5)+(3)(\dfrac{1}{4})+(\dfrac{1}{3})(\dfrac{1}{4})[/tex]

Answer:

The quotient is 1/4

Step-by-step explanation:

1/3 ÷ 4/3

The first step you have to do is change the division sign into multiplication. So that the denominator of 2nd term will become numerator and the numerator will become denominator.

Like:

1/3 * 3/4

Now you can cancel out 3 by 3

1 * 1/4

1/4

Thus the quotient is 1/4 ....

For this case we must find the quotient of the following expression:

[tex]\frac {\frac {1} {3}} {\frac {4} {3}}[/tex]

If we apply double C we have:

[tex]\frac {3 * 1} {3 * 4} =[/tex]

We cancel similar terms in the numerator and denominator and finally we have the quotient is:

[tex]\frac {1} {4}[/tex]

Answer:

[tex]\frac {1} {4}[/tex]

Answer:

(5,1)

(5,0)

Step-by-step explanation:

Vertical lines contain the same x-coordinate per any point on it's line.

So the x-coordinate of (5,-2) is 5.

We are looking for points that have the x-coordinate being 5.

(5,1)

(5,0)

Actually the equation for this line is x=5.

[tex]\huge{\boxed{\text{(5, 1)}}}\ \huge{\boxed{\text{(5, 0)}}}[/tex]

[tex]\text{A vertical line is a line where all of the x values (the first values) are the same.}[/tex]

[tex]\text{In this case, all answers with an x value of 5 are correct.}[/tex]

Answer:

Efficiency is the ratio of output work to input work.

Machine efficiency is the percent ratio of output work to input work, calculated by (Wout / Win) * 100, and accounts for real-world energy losses, making it always less than 100 percent.

The ratio of output work to input work expressed as a percent is known as the efficiency of a machine. This efficiency (Eff) can be calculated using the equation Eff = (Wout / Win) * 100, where Wout is the output work and Win is the input work. In the context of simple machines, work (W) is defined as the force (F) applied over a distance (d), thus W = F * d. While ideal mechanical advantage (IMA) does not consider losses like friction and is calculated using specific equations for each type of machine, efficiency takes into account real-world factors and is always less than 100 percent due to these energy losses.

Answer:

16

Step-by-step explanation:

х2 + 8x = 4

Take the coefficent of the x term, 8

Divide it by 2. 8/2 =4

Then square it, 4^2 = 16

Add this to both sides of the equation

x^2 +8x+16 = 4+16

Answer:

6/16 or 0.375 ..

Step-by-step explanation:

Each time the coin has two possible outcomes so tossing the coin four times

The sample space will be: 2^4 = 16

The sample space is: {HHHH, HTHH, THHH, HTHT , HHHT, HTTH, TTHH, THTH, HHTT, HHTH, TTTH, THHT ,HTTT, TTTT, TTHT, THTT}

Let A be the event that there are exactly two heads

A = {HTHT, HTTH, TTHH, THTH, HHTT, THHT}

n(A) = 6

So the probability of exactly two heads is:

P(A) = 6/16 or 0.375 ..

Answer:

3/8

Step-by-step explanation:

The person up there answered it right they just went too high with the numbers.

The graph of the quadratic parent function, y = x^2, is indeed a parabola and lies in quadrants I and II. It is not a straight line and doesn't occupy quadrants I and III.

The graph of the quadratic parent function, which is y = x^2, has specific characteristics, namely:

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Answer:

B.

Step-by-step explanation:

If f(-x)=f(x), then f is even.

If f(-x)=-f(x), then f is odd.

To determine if f(x)=3x^4+5x^2+1 is even or odd plug in -x like so:

f(x)=3x^4+5x^2+1

f(-x)=3(-x)^4+5(-x)^2+1

f(-x)=3x^4+5x^2+1

f(-x)=f(x)

So f is even.

You should keep in mind the following:

(-x)^odd=-(x^odd)

(-x)^even=x^even

Examples:

(-x)^81=-(x^81) since 81 is odd

(-x)^10=x^10 since 10 is even

Anyways, the student is right and f(-x)=f(x).

Answer:

The student's claim is true, because for any input of x, f(x)=f(−x).

Step-by-step explanation:

If a student says that the function f(x)=3x^4+5x^2+1 is an even function, the student's statement true  because for any input of x, f(x)=f(−x).

f(-x)=f(x) is even.

f(-x)=-f(x) is odd

Answer:

5 : 3

Step-by-step explanation:

Five A's

Three B's

Therefore, 5 : 3

You would not include the letters because a ratio is just a number.

Answer:

4√3.

Step-by-step explanation:

√48

= √(16 * 3)

= √16 * √3

= 4√3.

Answer:

Step-by-step explanation:

If two lines are parallel, their slopes are equal.

Next time, if you are given possible answer choices, please share them.

Answer:

The slopes of the two lines that are parallel, are equal.

Step-by-step explanation:

In order for two or more lines to be parallel their slopes have to be the same.

Multiply the total number of slices by the fraction he ate:

12 slices x 1/6 = 12/6 = 2

He ate 2 slices.

Answer:

2

Step-by-step explanation:

1/6 of 12 =

= 1/6 * 12

= 1/6 * 12/1

= (1 * 12)/(6 * 1)

= 12/6

= 2

Answer:

Discontinuities are created when the denominator of the rational expression equals zero (because division by zero is undefined). Graphically, this is usually represented by a dashed vertical line indicating a vertical asymptote.

Answer:

First part:

Set h(t) = 17and solve for t.

-16t²+ 58t + 7= 17

-16t² + 58t - 10 = 0

Solve this quadratic equation for t. You should get 2 positive solutions. The lower value is the time to reach 17 on the way up, and the higher value is the time to reach 17 again, on the way down.

Second part:

Set h(t) = 0 and solve the resulting quadratic equation for t. You should get a negative solution (which you can discard), and a positive solution. The latter is your answer.

Answer:

x < -2

Step-by-step explanation:

2|x| > 3x + 10

Divide both sides by 2.

|x| > 1.5x + 5

********************************************************

An absolute value inequality of the form

|X1| > X2

where X1 and X2 are expressions in x is solved by solving the compound inequality

X1 > X2 or X1 < -X2

********************************************************

Back to your problem.

|x| > 1.5x + 5

x > 1.5x + 5   or   x < -(1.5x + 5)

-0.5x > 5     or   x < -1.5x - 5

x < -10   or    2.5x < -5

x < -10    or    x < -2

Since x < -10 is included in x < -2, the solution is

x < -2

Answer:

[tex]\large\boxed{1.\ V=\dfrac{80\pi}{3}\ cm^3\approx83.73\ cm^3}\\\boxed{2.\ V=\dfrac{28\pi}{3}\ cm^3\approx29.31\ cm^3}\\\boxed{3.\ V=36\pi\ in^3\approx113.04\ cm^3}[/tex]

Step-by-step explanation:

The formula of a volume of a cone:

[tex]V=\dfrac{1}{3}\pi r^2H[/tex]

r - radius

H - height

[tex]\pi\approx3.14[/tex]

[tex]\bold{1.}\\\\r=4cm,\ H=5cm\\\\V=\dfrac{1}{3}\pi(4^2)(5)=\dfrac{1}{3}\pi(16)(5)=\dfrac{80\pi}{3}\ cm^3\approx\dfrac{(80)(3.14)}{3}=83.73\ cm^3[/tex]

[tex]\bold{2.}\\\\r=2cm,\ H=7cm\\\\V=\dfrac{1}{3}\pi(2^2)(7)=\dfrac{1}{3}\pi(4)(7)=\dfrac{28\pi}{3}\ cm^3\approx\dfrac{(28)(3.14)}{3}=29.31\ cm^3[/tex]

[tex]\bold{3.}\\\\r=6in,\ H=3in\\\\V=\dfrac{1}{3}\pi(6^2)(3)=\dfrac{1}{3}\pi(36)(3)=36\pi\ in^3\approx(36)(3.14)=113.04\ in^3[/tex]

Answer: 3 - [tex]\frac{c}{4}[/tex]

Step-by-step explanation:

2c - 8f = 24

2(c - 4f) = 2(12)

c - 4f = 12

4f = 12 - c

F = 3 - [tex]\frac{c}{4}[/tex]

Answer:

[tex]\Large \boxed{Y=5}[/tex]

Step-by-step explanation:

[tex]\textnormal{First, divide by 90 from both sides of the equation.}[/tex]

[tex]\displaystyle \frac{90y}{90}=\frac{450}{90}[/tex]

[tex]\textnormal{Solve to find the answer.}[/tex]

[tex]\displaystyle 450\div90=5[/tex]

[tex]\displaystyle y=5[/tex], which is our answer.

Hope this helps!

The value of Y in the equation '90 x Y = 450' can be found by isolating Y. This is done by dividing both sides of the equation by 90. Hence, Y equals 5.

In the mathematical equation

90 x Y = 450

, we are being asked to solve for Y. To solve for Y, we can use the basic algebraic principle of isolating the variable on one side of the equation. In this case, since we have 90 multiplied by Y equals 450, we want to isolate Y. We can do that by dividing both sides of the equation by 90. The equation now becomes

Y = 450/90

. By performing the division, we find that

Y equals 5

.

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