How many solutions does this equation have? 3x^2 - 6x + 4 = 0?

Ans:63

Exp:The angles is less than 90 so it cant be 92 or 121. It is also compare with the angle 58 but we can see it is not 58, so the only remaining logical answer would be 63.

Answer:

Here's a possible example:

Step-by-step explanation:

[tex]f(x) =\begin{cases} x & \quad x < 3\\x+3 & \quad x \geq 3\\\end{cases}[/tex]

Each piece is linear, so the pieces are continuous by themselves.

We need consider only the point at which the pieces meet (x = 3).

[tex]\displaystyle \lim_{x \longrightarrow 3^{-}} f(x) = \lim_{x \longrightarrow 3^{-}} x = 3\\\\\displaystyle \lim_{x \longrightarrow 3^{+}} f(x) = \lim_{x \longrightarrow 3^{+}} x+3 = 6\\\\f(3) = x + 3 = 6\\\\\displaystyle \lim_{x \longrightarrow 3^{-}} f(x) \neq f(3)[/tex]

The left-hand limit does not equal ƒ(x), so there is a jump discontinuity at x =3.

Final answer:

A piecewise function with a jump discontinuity at x = 3 could be f(x) = 2x for x < 3 and f(x) = 2x + 1 for x ≥ 3. It fails the 3-step test for continuity at x = 3 in the second step, as the limits on either side of the point x = 3 do not match.

Explanation:

To write the equation of a piecewise function with a jump discontinuity at x = 3, we can define one function for values of x less than 3, and another for values of x equal to or greater than 3. For instance:

Now, to determine where the piecewise function fails the 3-step test for continuity at x = 3, we assess the following criteria:

Therefore, the function has a jump discontinuity at x = 3 because it fails the second step of the 3-step test for continuity, where the left and right-hand limits are not equal.

Answer:

a) The equation is s = 64t - 16.1 t² + 3

b) The ball will take 1.99 seconds to reach its maximum height

c) The maximum height the ball will reach is 66.60 feet

d) The ball will be in the air for 4.02 seconds

Step-by-step explanation:

* Lets revise some rules of distance , velocity and time

- If the displacement is s , initial velocity is u , time is t and acceleration of

free fall is a , then the equation of the trajectory is

s = ut - 1/2 at² ⇒ upward thrown

∵ The acceleration of free fall a = 32.2 feet/sec²

∴ s = ut - 1/2 (32.2) t²

∴ s = ut - 16.1 t²

∵ The initial velocity is 64 feet/second

∴ s = 64t - 16.1 t²

∵ The ball is thrown from a height 3 feet

∴ s - 3 = 64t - 16.1 t² ⇒ add 3 to both sides

∴ s = 64t - 16.1 t² + 3

a) The equation is s = 64t - 16.1 t² + 3

- The ball will reach the maximum height when its velocity (v)

  reached to 0

∵ v = ds/dt

∵ s = 64t - 16.1 t² + 3

- The rule of differentiation

# y = ax^n ⇒ dy/dx = a(n) x^(n-1)

# y = ax ⇒ dy/dx = a

# y = a ⇒ dy/dx = 0

∴ ds/dt = 64 - 16.1(2) t + 0

∴ v = 64 - 32.2 t

∵ At maximum height v = 0

∴ 0 = 64 - 32.2 t ⇒ add 32.2 t to both sides

∴ 32.2 t = 64 ⇒ divide both sides by 32.2

∴ t = 1.987577 ≅ 1.99 seconds

b) The ball will take 1.99 seconds to reach its maximum height

- To find the maximum height substitute this value of t in the

  equation of trajectory

∵ s = 64t - 16.1 t² + 3

∴ s maximum = 64(1.99) - 16.1(1.99)² + 3 = 66.60

c) The maximum height the ball will reach is 66.60 feet

- To find the time that the ball in the air put s = 0, because the ball will

 return to the point of thrown

∵ s = 0

∵ s = 64t - 16.1 t² + 3

∴ 0 = 64t - 16.1 t² + 3 ⇒ multiply both sides by -1

∴ 16.1 t² - 64t - 3 = 0

- Use your calculator to factorize it and find the value of t

∴ t = 4.02 or -0.5

- We will refused the negative answer because there is no negative time

∴ t = 4.02

d) The ball will be in the air for 4.02 seconds

Use the intersecting chords theorem: the labeled angle (WVZ) between the given chords has measure that is the average of the two arcs the chords intercept (WZ and XY):

[tex]81^\circ=\dfrac{m\widehat{XY}+52^\circ}2\implies m\widehat{XY}=110^\circ[/tex]

The requried measure of the arc XY is 110°. Option D is correct.

An arc is a portion of the circumference of a circle. It is defined by two endpoints on the circle and all the points on the circle between these endpoints. The length of an arc is proportional to the measure of the central angle that subtends it.

Here,
To use the intersecting chords theorem,
we can state that the measure of the labeled angle (WVZ) between the given chords is equal to the average of the measures of the two arcs intercepted by the chords, namely WZ and XY.

81 = mWZ+ mXY/2
81 = 52 + mXY / 2
mXY = 110°

Thus, the requried measure of the arc XY is 110°. Option D is correct.

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ANSWER

[tex]\frac{x - 4}{2x - 2} [/tex]

EXPLANATION

The given expression is;

[tex] \frac{2 {x}^{2} + 5x + 3}{ {x}^{2} - 3x - 4} \div \frac{4 {x}^{2} + 2x - 6}{ {x}^{2} - 8x + 16} [/tex]

We factor to obtain;

[tex] \frac{(x + 1)(2x + 3)}{(x - 4)(x + 1)} \div \frac{2(x - 1)(2x + 3)}{(x - 4)(x - 4)} [/tex]

Multiply by the reciprocal of the second fraction

[tex]\frac{(x + 1)(2x + 3)}{(x - 4)(x + 1)} \times \frac{(x - 4)(x - 4)}{2(x - 1)(2x + 3)} [/tex]

Cancel out common factors to get,

[tex]\frac{1}{1} \times \frac{(x - 4)}{2(x - 1)} [/tex]

[tex]\frac{x - 4}{2x - 2} [/tex]

Answer:

X-4/2x-2

Step-by-step explanation:

Answer:

The answer is D

Step-by-step explanation:

for every increase in the product sold, the earnings increase by 300 respectively

Answer:

(0, 6)

Step-by-step explanation:

The given point A has coordinates (4,-2).

The mapping for a reflection over the line y=k, is given by:

[tex](x,y)\to (x,2k-y)[/tex]

Therefore the line y=2 is

[tex](4,-2)\to (4,2(2)--2)[/tex]

[tex](4,-2)\to (4,4+2)[/tex]

[tex](4,-2)\to (4,6)[/tex]

When this point is again reflected over the line x=2, we use the mapping

[tex](x,y)\to (2k-xx,y)[/tex]

[tex](4,6)\to (2(2)-4,6)[/tex]

[tex](4,6)\to (4-4,6)[/tex]

[tex](4,6)\to (0,6)[/tex]

Answer:

0,6

Step-by-step explanation:

1) If f(x) = -3x⁴ - 2x³ + 3x²

  If g(x) = 3x⁴ - 4x³ + x²

Set the equation:

f(x) + g(x) = (-3x⁴ - 2x³ + 3x²) + (3x⁴ - 4x³ + x²)

Rearrange from greatest power sign to the least:

f(x) + g(x) = -3x⁴ + 3x⁴ - 2x³ - 4x³ + 3x² + x²

Combine like terms (terms with the same amount of variables):

f(x) + g(x) = (-3x⁴ + 3x⁴) + (-2x³ - 4x³) + (3x² + x²)

f(x) + g(x) = (0) + (-6x³) + (4x²)

f(x) + g(x) = -6x³ + 4x²

B) -6x³ + 4x² is your answer.

__________________________________________________________

2) If s(x) = 2x² + 3x - 4

   If t(x) = x + 4

Set the equation:

s(x) * t(x) = (2x² + 3x - 4) * (x + 4)

To solve for multiplication, choose a parenthesis. Distribute each term within that parenthesis to all terms within the other.

s(x) * t(x) = 2x²(x + 4) + 3x(x + 4) - 4(x + 4)

Simplify.

s(x) * t(x) = 2x³ + 8x² + 3x² + 12x - 4x - 16

Combine like terms.

s(x) * 5(x) = 2x³ + 11x² + 8x - 16

A) 2x³ + 11x² + 8x - 16 is your answer.

~

Answer:

True

Step-by-step explanation:

The hypotenuse angle theorem, also known as the HA theorem, states that "If the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and an acute angle of another right triangle, then the two triangles are congruent."

In triangles MNP and QRS:

Then, triangles MNP and PRS are congruent by HA theorem.

True

Answer:

True (just did it on a pex)

Step-by-step explanation:

Step-by-step Answer:

One of the properties of a least-squares regression line (line of best fit) is that the line always passes through the point (xbar, ybar).

Assuming the given "line of best fit" is a least-squares line, then we are given

a slope m=1.885 passing through (x0,y0)=(3.448,12.318).

Applying the standard point-slope formula:

(y-y0) = m (x-x0)

we get

y-12.318 = 1.885(x-3.448)

Expand and simplify,

y=1.885x -1.885*3.448 + 12.318, or

y=1.885(x) + 5.81852

(numbers to be rounded as precision dictates).

To find the y-intercept of the line of best fit, substitute the mean x and y values and the slope into the equation y = mx + b and solve for b. In this case, the y-intercept is 5.820.

To calculate the y-intercept of the line of best fit when you know the slope and the mean values of the x-coordinates and y-coordinates, you can use the formula for the equation of a line, which is y = mx + b, where m is the slope and b is the y-intercept.

Given:

We can substitute the means into the line equation:

12.318 = 1.885(3.448) + b

Now solve for b:

12.318 = 6.49836 + b

b = 12.318 - 6.49836

b = 5.81964

Therefore, the y-intercept b to three decimal places is 5.820.

Answer:

[tex]\large\boxed{\left(-\dfrac{11}{2};\ -\dfrac{11}{2}\right)}[/tex]

Step-by-step explanation:

The formula of a midpoint of the segment"

[tex]\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)[/tex]

We have the points W(-3, -7) and X(-8, -4).

Substitute:

[tex]x=\dfrac{-3+(-8)}{2}=\dfrac{-11}{2}\\\\y=\dfrac{-7+(-4)}{2}=\dfrac{-11}{2}[/tex]

The coordinates of the midpoint of a line segment with endpoints (-3, -7) and (-8, -4) are (-5.5, -5.5) using the midpoint formula.

The subject of this question is Mathematics, specifically dealing with geometry. The student is asked to find the midpoint of a line segment whose endpoints are given. The coordinates of the endpoints of the line segment are W(-3, -7) and X(-8, -4).

The formula to calculate the coordinates of a midpoint in a Cartesian plane is M = [(x1 + x2)/2, (y1 + y2)/2], where M denotes the midpoint, (x1, y1) and (x2, y2) are the coordinates of the endpoints of the line segment.

Thus, the midpoint M of the line segment WX is calculated as follows: M = [(-3 -8)/2, (-7 -4)/2] =  [-11/2, -11/2]. So, the coordinates of the midpoint of the line segment WX are (-5.5, -5.5).

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Jenna is correct because the square root of a rational number can still be irrational.

Take for example the square root of 2. It is an irrational number than goes 1.41421...

If you multiply just the first however many digits of the result by itself, you will never end up with a perfect 2, because the square root is irrational.

Answer:

Jenna is correct because not all square roots are rational.

Step-by-step explanation:

Answer:  D) (-5, 1)

Step-by-step explanation:

Inverse is when the x's and y's are swapped.

f(x) has the coordinate (1, -5) --> the inverse of that is (-5, 1), which is option D.

Answer:

170 ft²

Step-by-step explanation:

First let's calculate the height of this trapezoid.  Call it 'h.'  Look at the triangle on the right; the base is equal to (22 ft - 12 ft), or (10 ft).  Using the tangent function, we can find h:

                    h

tan 45° = ---------- = 1  and so we know that h = 10 ft

                  10 ft

The formula for the area of a trapezoid is

A = (average length)*(width)

Here we have:

A = [ (12 ft + 22 ft) / 2 ] * 10 ft, or

A  =           (17 ft)*(10 ft) = 170 ft²

Yes.

The triangle inequality theorem states that a triangle is possible if the sum of two sides is larger than the 3rd side.

In this case, the sides are 4, 5 and 6.

4+5 is bigger than 6

4 + 6 is bigger than 5

5 + 6 is bigger than 4.

The sum of any 2 sides is always larger than the 3rd side, so this triangle is possible.

-------------------------------------------------------

Answer:   Yes

Answer:

(x,12x-18)

Step-by-step explanation:

Answer:

Check attached graph

Step-by-step explanation:

Given equation of the parabola is [tex]y=-2x^2+12x-14[/tex].

Nowe we need to use the parabola tool to graph the quadratic function. Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.

Compare Given equation with [tex]y=ax^2+bx+c[/tex] we get: a=-2 and b=12

then x-coordinate of vertex [tex]=x=-\frac{b}{2a}=-\frac{12}{2\left(-2\right)}=3[/tex]

plug x=3 into given function

[tex]y=-2x^2+12x-14[/tex]

[tex]y=-2(3)^2+12(3)-14=4[/tex]

Hence vertex is (3,4).

Plug any x-value say x=0 into given function to find other point

[tex]y=-2(2)^2+12(2)-14=2[/tex]

Hence second point is (2,2)

now graph the parabola using both points as shown below:

Answer:

see explanation

Step-by-step explanation:

All of these questions use the external angle theorem, that is

The external angle of a triangle is equal to the sum of the 2 opposite interior angles.

18

∠3 = 43° + 22° = 65°

19

∠2 + 71 = 92 ( subtract 71 from both sides )

∠2 = 21°

20

90 + ∠4 = 123 ( subtract 90 from both sides )

∠4 = 33°

21

2x - 15 + x - 5 = 148

3x - 20 = 148 ( add 20 to both sides )

3x = 168 ( divide both sides by 3 )

x = 56

Hence ∠ABC = x - 5 = 56 - 5 = 51°

22

2x + 27 + 2x - 11 = 100

4x + 16 = 100 ( subtract 16 from both sides )

4x = 84 ( divide both sides by 4 )

x = 21

Hence ∠JKL = 2x - 11 = (2 × 21) - 11 = 42 - 11 = 31°

Answer:

  7/4 yard

Step-by-step explanation:

36 is a suitable common denominator for expressing these fractions. All measures are in yards.

  2/3 + 4/9 + 23/36 = (12·2)/(12·3) + (4·4)/(4·9) + 23/36

  = 24/36 + 16/36 + 23/36

  = 63/36 = (9·7)/(9·4)

  = 7/4 = 1 3/4 . . . . . yards

Answer:

C. x = 2, and x = -2

Answer:  C) x = 2 and x = -2

Step-by-step explanation:

Vertical Asymptotes are restrictions on the x-values.

Since the denominator cannot equal zero, then any x-value that makes the denominator equal to zero is a vertical asymptote.

x² - 4 = 0

(x - 2)(x + 2) = 0

x - 2 = 0    x + 2 = 0

  x = 2        x = -2

Margret sold a total of 3,332 meatballs on Friday and Saturday by adding the meatballs sold on each day (1,392 on Friday and 1,940 on Saturday).

To find out how many meatballs Margret sold on Friday and Saturday combined, we simply add the number she sold on each day. On Friday, she sold 1,392 meatballs and on Saturday, she sold 1,940 meatballs.

The total number of meatballs sold over the two days is:

1,392 (meatballs on Friday)
+ 1,940 (meatballs on Saturday)
3,332 (total meatballs)

So, Margret sold a total of 3,332 meatballs on Friday and Saturday.

Answer:

1/4, 0.25, 25%

Step-by-step explanation:

There are 8 letters in total and 2 K's out of those 8. Therefore the fraction is 2/8, and simpfied it would be 1/4. 1/4 is equal to 0.25 and 25%.

Answer:

3/4,  0.75, 75%.

Step-by-step explanation:

J, K , L, J, K, M, N, P.

There are 8 letters and 2 of them are K, therefore 6 of them are not K.

Probability ( Not picking K) =  6/8

= 3/4 or 0.75 or 75%.

Answer:

2x^3 - 2x^2  - 12x

Step-by-step explanation:

2x(x - 3)(x + 2)

= 2x ( x^2 + 2x -3x - 6)

= 2x (x^2 - x - 6)

= 2x^3 - 2x^2  - 12x (answer).

Answer:

Step-by-step explanation:

Find the product

2x(x - 3)(x + 2)

OA. 4x - 1

B. 2x3 -X-6 Find the product

2x(x - 3)(x + 2)

OA. 4x - 1 Find the product

2x(x - 3)(x + 2)

OA. 4x - 1

B. 2x3 -X-6

C. 2x3 - 2x2 - 12x

2x3-12x|

B. 2x3 -X-6

C. 2x3 - 2x2 - 12x

2x3-12x|

C. 2x3 - 2x2 - 12x

2x3-12x|Find the product

2x(x - 3)(x + 2)

OA. 4x - 1

B. 2x3 -X-6

C. 2x3 - 2x2 - 12x

2x3-12x|

Answer:

  (1, 1) is NOT a solution

Step-by-step explanation:

The only point of intersection of the graphs is (0, 2). The point of intersection is the solution to the system of equations. (1, 1) is not the point of intersection, so is NOT the solution to the system of equations.

The point (1,1) is not a solution to the system of equations because, when we substitute the coordinates into the equations, it matches the second equation but not the first.

To determine whether point (1,1) is a solution to the system of equations, we need to substitute the x and y values of the point into each equation and see if they produce true statements.

The first equation in the system is '3 times x plus 2', which we can write as 3x + 2. Substituting x = 1 in this equation gives us 3*1 + 2 = 5, which is not equal to the y-coordinate (1) of our input point.

The second equation is the |x - 1| + 1, which refers to the absolute value of (x minus 1) plus one. If we input x = 1, we get |1 - 1| + 1 = 1, which equals the y-coordinate (1) of our point. However, because the point didn't satisfy both equations, (1,1) is not a solution to the system.

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Answer:

0.95

Step-by-step explanation:

This is what Algebra Nation told me, I just want to help get the answer correct

take the square root of 36 and subtract 2 because √36= 6-2=4x

Answer:

take the square root of 36 and subtract 2 because √36= 6-2=4x

Step-by-step explanation:

Check the picture below.

Answer:

The correct answer is 23

Step-by-step explanation:

Answer: 5,000

Step-by-step

Answer:

5,000

Step-by-step explanation:

just got my paper graded

Since p = x² - 7, you can substitute/plug in p for x² - 7

So:

(x² - 7)² - 4x² + 28 = 5

(p)² - 4x² + 28 = 5      You can factor out -4 from (-4x² + 28)

p² - 4(x² - 7) = 5        Plug in p

p² - 4p = 5        Subtract 5

p² - 4p - 5 = 0        Your answer is C

To find an equation equivalent to (x^2-7)-4x^2+28 in terms of p, substitute x^2-7 with p. The equation equivalent to (x^2-7)-4x^2+28 in terms of p is -4x^2+p+28.

To find an equation equivalent to (x^2-7)-4x^2+28 in terms of p, we can substitute x^2-7 with p. So we have (p)-4x^2+28. Now, we combine like terms by adding the coefficients of p and -4x^2, which gives us -4x^2+p+28.

Answer:

Step-by-step explanation:

The (x - 4) indicates side-to-side movement, and the -3 at the end indicates up and down movement.  This log graph has moved 4 units to the right (x - (4)) and down 3 units (-3)

Final answer:

The transformation consists of a horizontal shift to the right by 4 units and a vertical shift downward by 3 units from the parent function f(x) = log x to g(x) = log(x - 4) - 3.

Explanation:

The transformation of the parent function f(x) = log x to g(x) = log(x - 4) - 3 involves a horizontal shift to the right by 4 units and a vertical shift downward by 3 units. This is because for the horizontal shift, the logarithmic function is now evaluating (x - 4) instead of x, indicating a move to the right on the x-axis by 4 units. Similarly, subtracting 3 from the whole function log(x - 4) indicates that every value of the function will be decreased by 3 units on the y-axis.

7068.58 cubic feet is the volume