The vertex of ABC is:
А
В
C

Answer:

x = -3/4 or x = 3

Step-by-step explanation:

Solve for x over the real numbers:

(-4 x - 3) (x - 3) = 0

Hint: | Find the roots of each term in the product separately.

Split into two equations:

-4 x - 3 = 0 or x - 3 = 0

Hint: | Look at the first equation: Divide both sides by the sign of the leading coefficient of -4 x - 3.

Multiply both sides by -1:

4 x + 3 = 0 or x - 3 = 0

Hint: | Isolate terms with x to the left hand side.

Subtract 3 from both sides:

4 x = -3 or x - 3 = 0

Hint: | Solve for x.

Divide both sides by 4:

x = -3/4 or x - 3 = 0

Hint: | Look at the second equation: Solve for x.

Add 3 to both sides:

Answer: x = -3/4 or x = 3

Answer:

lesser x = -3/4

greater x =3

Step-by-step explanation:

h(x) = (-4x – 3)(x – 3)

Set the function equal to zero to find the zeros

0 = (-4x – 3)(x – 3)

Using the zero product property

0 = (-4x – 3)   0=(x – 3)

Solve each  equation

3 = -4x          3 =x

-3/4=x            3 =x

lesser x = -3/4

greater x =3

Answer:

me me me omg

Step-by-step explanation:

Answer:

108

Step-by-step explanation:

i think that's the answer not sure

7 L of one solution is mixed with 3 L of another, making a new solution with a total volume of 10 L and concentration 29%. This means the new solution contains

(10 L) * 29% = (10 L) * 0.29 = 2.9 L

of acid.

Let the concentration of the first solution be c%. Each liter of the 15% acid solution contributes 0.15 L, and each liter of the solution of unknown concentration contributes 0.01c L of acid. To end up with a total of 2.9 L of acid, we would get

7 * (0.01c L) + 3 * (0.15 L) = 2.9 L

Solve for c (we can omit the units):

0.07c + 0.45 = 2.9

0.07c = 2.45

c = 35

So the first solution has a concentration of 35%.

The transfer functions for the given systems represented in state space are: a. G(s) = (s+5)/(s²+ s - 10), b. G(s) = (3s² - 13s + 2)/(s³ - 3s² + 4s + 10) and c. G(s) = (7s² - 10s + 24)/(s³ + 9s²+ 28s + 20)

To find the transfer function G(s) = Y(s)/R(s) for each of the given systems represented in state space, we can use the formula:
G(s) = C(sI - A)^-1B + D
where A, B, C, and D are matrices obtained from the given state space representation. Let's find the transfer function for each system:

a. Given state space representation:
x = [ 0  0  -3 ]   x + [ 0 ]   r
       [ 1  0  -2 ]        [ 0 ]
       [ 0  1  -5 ]        [ 0 ]

Output equation: y = [ 1  0  0 ]  x

To find the transfer function, we need to calculate the matrices A, B, C, and D.

A = [ 0  0  -3 ]
      [ 1  0  -2 ]
      [ 0  1  -5 ]

B = [ 0 ]
      [ 0 ]
      [ 0 ]
C = [ 1  0  0 ]
D = [ 0 ]
Now, we can substitute these matrices into the transfer function formula:
G(s) = C(sI - A)^-1B + D

Calculating (sI - A):

sI - A = [ s   0   0 ] - [ 0  0  -3 ] = [ s   0    3 ]
            [ 0   s   0 ]     [ 1  0  -2 ]      [ -1  s   2 ]
            [ 0   0   s ]     [ 0  1  -5 ]      [ 0   -1  s+5 ]

Calculating (sI - A)^-1:

(sI - A)^-1 = [ (s+5)/(s² + s - 10)    3/(s² + s - 10)    3/(s+ s² - 10) ]
                       [ (-1)/(s² + s - 10)    s/(s² + s - 10)    2/(s² + s - 10) ]
                       [ 0   -1/(s² + s - 10)    (s+5)/(s² + s - 10) ]

Calculating C(sI - A)^-1B:
C(sI - A)^-1B = [ 1  0  0 ] [ (s+5)/(s²+ s - 10)    3/(s²+ s - 10)    3/(s²+ s - 10) ] [ 0 ] = (s+5)/(s²+ s - 10)
Finally, adding D:
G(s) = (s+5)/(s² + s - 10) + 0 = (s+5)/(s²+ s - 10)

b. Given state space representation:
x = [ 2  0  -3 ]   x + [ 1 ]   r
       [ -3  5  -5 ]        [ 4 ]
       [ -8  3  -4 ]        [ 6 ]

Output equation: y = [ 1  3  6 ]  x

Following the same steps as above, we find:

A = [ 2  0  -3 ]
      [ -3  5  -5 ]
      [ -8  3  -4 ]

B = [ 1 ]
      [ 4 ]
      [ 6 ]

C = [ 1  3  6 ]

D = [ 0 ]

Calculating (sI - A):

sI - A = [ s-2   0    3 ]
            [ 3   s-5   5 ]
            [ 8   -3   s+4 ]

Calculating (sI - A)^-1:
(sI - A)^-1 = [ (s+5)/(s³ 3s² + 4s + 10)    3/(s³ - 3s² + 4s + 10)    3/(s³ - 3s²+ 4s + 10) ]
                       [ (-3)/(s³ - 3s² + 4s + 10)    (s+2)/(s³ - 3s²+ 4s + 10)   5/(s³ - 3s²+ 4s + 10) ]
                       [ 8/(s³- 3s²+ 4s + 10)   -3/(s^3 - 3s² + 4s + 10)    (s-5)/(s³ - 3s² + 4s + 10) ]

Calculating C(sI - A)^-1B:

C(sI - A)^-1B = [ 1  3  6 ] [ (s+5)/(s³- 3s² + 4s + 10)    3/(s³ - 3s² + 4s + 10)    3/(s³ - 3s² + 4s + 10) ] [ 1 ] = (3s² - 13s + 2)/(s³ - 3s² + 4s + 10)

Finally, adding D:

G(s) = (3s² - 13s + 2)/(s³ - 3s² + 4s + 10) + 0 = (3s² - 13s + 2)/(s³- 3s²+ 4s + 10)

c.  Given state space representation:
x = [ 3  1  -3 ]   x + [ 5 ]   r
       [ -5  -8  -6 ]        [ -3 ]
       [ 2  7  2 ]        [ 2 ]

Output equation: y = [ 0  5  2 ]  x

Following the same steps as above, we find:

A = [ 3  1  -3 ]
      [ -5  -8  -6 ]
      [ 2  7  2 ]

B = [ 5 ]
      [ -3 ]
      [ 2 ]

C = [ 0  5  2 ]

D = [ 0 ]

Calculating (sI - A):

sI - A = [ s-3   -1    3 ]
            [ 5   s+8   6 ]
            [ -2   -7   s-2 ]

Calculating (sI - A)^-1:

(sI - A)^-1 = [ (s² - 6s + 9)/(s³ + 9s² + 28s + 20)    (-s+2)/(s³ + 9s² + 28s + 20)    (-3)/(s^3 + 9s² + 28s + 20) ]
                       [ (-5)/(s³+ 9s² + 28s + 20)    (s²- 10s + 4)/(s³ + 9s² + 28s + 20)    (-6)/(s³ + 9s² + 28s + 20) ]
                       [ (2)/(s³+ 9s² + 28s + 20)   (7)/(s³+ 9s² + 28s + 20)    (s² - 8s + 6)/(s³+ 9s² + 28s + 20) ]

Calculating C(sI - A)^-1B:

C(sI - A)^-1B = [ 0  5  2 ] [ (s- 6²s + 9)/(s³ + 9s² + 28s + 20)    (-s+2)/(s³ + 9s² + 28s + 20)    (-3)/(s³ + 9s² + 28s + 20) ] [ 5 ] = (7s² - 10s + 24)/(s³+ 9s² + 28s + 20)

Finally, adding D:

G(s) = (7s² - 10s + 24)/(s³ + 9s² + 28s + 20) + 0 = (7s²- 10s + 24)/(s³ + 9s²+ 28s + 20)

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The conclusion is that the given series diverges.

The given series 1, 5, 5, 5, 7.8, 5 + 9/2, 11 is an alternating series. So, we will determine if it converges or diverges using the alternating series test. We will write the answer in the main part. The alternating series test:

Let a1,a2,a3,...,an be a sequence of positive numbers, then the series Σ(-1)^n+1*a(n) is called an alternating series.

The alternating series test states that if a(n) is a decreasing sequence and limn→∞a(n)=0, then the series converges. Conversely, if a(n) does not decrease to 0, the series diverges.

Alternating series test: The given series 1, 5, 5, 5, 7.8, 5 + 9/2, 11 is an alternating series. So, we will determine if it converges or diverges using the alternating series test. We notice that 7.8 is greater than 5 + 9/2. So, the sequence is not decreasing. Therefore, we cannot use the alternating series test.

Instead, we will use the nth term divergence test.

nth term divergence test: Let Σa(n) be a series, then if limn→∞a(n)≠0, then the series diverges. If we write the terms of the given series, we obtain 1, 5, 5, 5, 7.8, 5 + 9/2, 11.

The nth term of the series is given by an= {1, 5, 5, 5, 7.8, 5 + 9/2, 11}.

So, limn→∞an≠0. Hence, by nth term divergence test, the series diverges.

Therefore, the conclusion is that the given series diverges.

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Given data,

Of the 50 students in the cafeteria

7 have red hair.

Total number of students = 750

To find:

The proportion that could be used to predict the number of students who have red hair.

Let us assume the number of students who have red hair = x

The ratio of student having red hair to the total number of students are

                           \(Ratio (1) = \frac{7}{50}\)

                           \(Ratio (2) = \frac{x}{750}\)

The number of students having red hair is proportional to the total number of students. So, the above ratios are equal.

                                    \(\frac{x}{750} = \frac{7}{50}\)

Cross multiplication,

                                    50x = 7 * 750

                                     50x = 5250

                                          x = 5250/50

                                          x = 105

Therefore,

The required equation is \(\frac{x}{750} = \frac{7}{50}\)  and the number of students who have red hair is 105.

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Answer:

588 units^2

Step-by-step explanation:

To find the area of the enlarged rectangle, first find the length and width of the enlarged rectangle.

This is 3.5 multiplied by their original measures:

Length = 3.5 x 8 = 28

Width = 3.5 x 6 = 21

Now, area =. LxW = 588 units^2

Hope this helps

Answer:

588 units squared

Step-by-step explanation:

We have a rectangle that has dimensions 8 units by 6 units.

From the problem, we know that this rectangle has been enlarged by a scale of 3.5. Essentially, to obtain the dimensions of the new, bigger rectangle, we multiply the current length (8 units) by 3.5 and the current width (6 units) by 3.5:

new length = 8 * 3.5 = 28 units

new width = 6 * 3.5 = 21 units

Given this, we can now calculate the area.

The area of a rectangle is denoted by A = lw, where l is the length and w is the width.

Here, the length is l = 28 and the width is w = 21. Plug these in:

A = lw

A = 28 * 21 = 588

The answer is thus 588 units squared.

~ an aesthetics lover

Answer:

The correct explanation is option B;

B. ∠L ≅ ∠L  By Reflexive Prop. ≅.

Since \(\overline {OP}\) ║ \(\overline {MN}\), ∠LOP ≅ ∠LMN by the Corr. ∠s Post. Therefore, ΔLOP ~ ΔLMN by AA ~. OP = 2 and MN = 6

Step-by-step explanation:

The given parameters are;

\(\overline {LP}\) = 5

\(\overline {NP}\) = 10

\(\overline {LN}\) = \(\overline {LP}\) + \(\overline {NP}\) = 15

\(\overline {OP}\) = x - 3

\(\overline {MN}\) = x + 1

A two column proof is presented as follows;

Statement    \({}\)      Reason

∠L ≅ ∠L     \({}\)        By Reflexive property of congruency

\(\overline {OP}\) ║ \(\overline {MN}\)     \({}\)     Given

∠LOP ≅ ∠LMN \({}\)  By the Corresponding angles Postulate

Therefore

ΔLOP ~ ΔLMN \({}\)  By AA similarity Postulate

Where we have that ΔLOP and ΔLMN, we get;

\(\overline {OP}\)/\(\overline {MN}\)  = \(\overline {LP}\)/\(\overline {LN}\) = 5/15 = 1/3

∴ (x - 3)/(x + 1) = 1/3

3·(x - 3) = 1·(x + 1)

3·x - 9 = x + 1

3·x - x = 1 + 9 = 10

2·x = 10

x = 10/2 = 5

x = 5

\(\overline {OP}\) = (x - 3) = 5 - 3 = 2

\(\overline {OP}\) = 2

\(\overline {MN}\) = x + 1 = 5 + 1 = 6

\(\overline {MN}\) =  6

Therefore, the correct option is ∠L ≅ ∠L  By Reflexive Prop. ≅.

Since \(\overline {OP}\) ║ \(\overline {MN}\), ∠LOP ≅ ∠LMN by the Corr. ∠s Post. Therefore, ΔLOP ~ ΔLMN by AA ~. OP = 2 and MN = 6.

Answer:

I think that the common factor in the given algebraic is a-b

The given function f(x) = 16^x is an exponential function.

An exponential function is a mathematical function in which an independent variable appears in the exponent. In this case, the base of the function is 16, and the variable x is the exponent.

In the given function f(x) = 16^x, the variable x represents the exponent to which 16 is raised. As x increases, the function value grows rapidly, indicating exponential growth. The base of 16 signifies that the function is being multiplied by 16 for each unit increase in the exponent.

In contrast, a linear function has a constant rate of change, and a quadratic function has a squared term. The given function does not involve a linear relationship or a squared term, which confirms that it is not a linear or quadratic function.

Therefore, based on the given form f(x) = 16^x and the exponential growth nature of the function, we can classify it as an exponential function.

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The domain and range of the graph above include the following:

A. Domain: All real numbers.

F. Range: y ≤ 0.

In Mathematics and Geometry, a domain is the set of all real numbers that defines a particular function (equation).

In Mathematics and Geometry, the horizontal part of any graph is used for representing all domain values and they're both read and written from smaller (minimum) to larger (maximum) numerical values, which is from the left of any graph to the right.

By critically observing the graph shown of this quadratic function, we can logically deduce the following domain and range:

Domain = [-∞, ∞] or all real numbers.

Range = [0, -∞] or y ≤ 0.

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Answer: 5x

Step-by-step explanation:

5x + 3x = 8x

Answer: Question

find the missing term in the equation below (?+5)+(3x-2)=8x+3

(5x+5)+(3x-2)=8x+3

5x+5+3x-2

5x+3x+5-2

8x+3

therefore, answer proved

PLZ ACCEPT MY EFFORT

5 STAR +THANKS  :(

Answer:

l think da answer iz 1323

Answer:

A bicycle

Step-by-step explanation:

because its the only one that is manually powered, you use your feet to peddle whereas all the others answer use an engine of sorts and dont generate kinetic energy

Answer:

A bicycle

Step-by-step explanation:

Step-by-step explanation:

Check the attached photo out

The equation of a parabola with a given focus and directrix is:

x^2 - 2ax + 2by + (a^2 + b^2 - c^2) = 0

In this equation, (a, b) represents the coordinates of the focus, and c represents the y-coordinate of the directrix. This equation describes a parabola where all points on the parabola are equidistant from the focus and the directrix.

To write the equation of a parabola with a given focus and directrix, we can use the geometric definition of a parabola. A parabola is the set of all points that are equidistant from the focus and the directrix.

Let's assume the focus is denoted as F(a, b) and the directrix is a horizontal line given by y = c. The vertex of the parabola is at the midpoint between the focus and the directrix, which is V(a, (b + c) / 2).

The distance from any point (x, y) on the parabola to the focus F(a, b) is given by the distance formula:

sqrt((x - a)^2 + (y - b)^2)

The distance from the point (x, y) on the parabola to the directrix y = c is given by |y - c|.

According to the definition of a parabola, these two distances are equal. Thus, we can set up the equation:

sqrt((x - a)^2 + (y - b)^2) = |y - c|

Squaring both sides of the equation eliminates the square root:

(x - a)^2 + (y - b)^2 = (y - c)^2

Expanding and rearranging the terms:

x^2 - 2ax + a^2 + y^2 - 2by + b^2 = y^2 - 2cy + c^2

Simplifying and canceling out the y^2 terms:

x^2 - 2ax + a^2 + b^2 - 2by = c^2 - 2cy

Rearranging the terms to obtain the standard form of the equation:

x^2 - 2ax + 2by + (a^2 + b^2 - c^2) = 0

Thus, the equation of the parabola with focus F(a, b) and directrix y = c is given by:

x^2 - 2ax + 2by + (a^2 + b^2 - c^2) = 0

Complete Question - Write the equation of a parabola with focus F(a, b) and directrix given by y = c.

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Step-by-step explanation:

20%=cows 0.4(40%)=goat 40%=sheep

if 40%sheep=40 sheeps

20% cow=x

20%×40=40%×x

8=40%x

x=8/40%

x=20

..so there are 20 cows

sorry...not sure

Answer:

There are 20cows

Step-by-step explanation:

20%=0.2 of cows

0.4=goats

1-(0.2+0.4)=0.4 are sheep

Using ratio and proportion,

0.2/0.4×40=20

The number of masks Elizabeth kept on the wall is 273.

Elizabeth has a mask collection of 420 masks.  She keeps 65 percent of the masks on her wall.

The number of mask she keeps on the wall can be calculated as follows:

Therefore,

number of mask she keeps on the wall = 65 percent of total mask collection

number of mask she keeps on the wall = 65% of 420

number of mask she keeps on the wall = 65 / 100 × 420

number of mask she keeps on the wall = 27300 / 100

Therefore,

number of mask she keeps on the wall = 273

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The width of the parallelogram can be any value greater than or equal to 14 feet.

What is parallelogram ?

A parallelogram is a four-sided polygon with opposite sides that are parallel. It has opposite angles that are equal and opposite sides that are equal in length. A special cases of parallelograms are rectangles, which have four right angles, and squares, which have four right angles and all sides are equal in length.

P = 2l + 2w >= 40

where P is the perimeter, l is the length and w is the width.

Substituting the given value for the length, we get ,

2(6) + 2w >= 40

Simplifying and solving for w ,

12 + 2w >= 40

2w >= 28

w >= 14

Therefore, the width of the parallelogram can be any value greater than or equal to 14 feet.

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The length of the diagonal of the rectangular ceiling can be found using the Pythagorean theorem. Therefore, the length of the diagonal of the ceiling is the square root of the sum of the squares of the lengths of its sides, which is the square root of (16^2 + 12^2) = 20 meters (rounded to the nearest meter). Savannah will need at least 20 meters of garland to reach from one corner of the ceiling to the opposite corner.

In a rectangular ceiling, the diagonal is the longest line segment that can be drawn from one corner of the ceiling to the opposite corner. It forms a right triangle with the two sides of the rectangle as its legs. The Pythagorean theorem can be used to find the length of the diagonal, which is also the minimum length of garland needed to span the distance between the two corners.

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Square tile with measure of each side is 16inches have area equals to 1652 centimeters( round off to nearest square centimeters).

As given in the question,

Measure of each side length of a square tile = 16 inches

Conversion

1 inch = 2.54 centimeters

16 inches = ( 16 × 2.54 )centimeters

                = 40.64centimeters

Area of a square tile is :

= ( Side length ) × ( Side length)

= (40.64) × (40.64)

= 1651.6096 centimeters

= 1652 centimeters ( round off to nearest square centimeters)

Therefore, the area of a square tile with given measure of each side is equal to 1652 centimeters ( round off to nearest square centimeters).

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The tangential component of the acceleration vector is 36j.
The normal component of the acceleration vector is 18i / √(1 + 4t^2).

Tangential component: The tangential component of the acceleration vector is given by the derivative of the velocity vector. The velocity vector is the derivative of the position vector. In this case, the position vector is r(t) = 6(3t - t^3)i + 18t^2j. Taking the derivative of the position vector, we get the velocity vector v(t) = 18i + 36tj. Taking the derivative of the velocity vector, we find that the tangential component of the acceleration vector is a(t) = 0i + 36j. Therefore, the tangential component of the acceleration vector is 36j.

Normal component: The normal component of the acceleration vector can be found by taking the derivative of the velocity vector with respect to arc length. The magnitude of the velocity vector is the rate of change of arc length, so we can find the arc length s(t) by integrating the magnitude of the velocity vector. In this case, the magnitude of the velocity vector is |v(t)| = √(18^2 + (36t)^2) = 18√(1 + 4t^2). Integrating this expression, we find that the arc length is s(t) = 18t√(1 + 4t^2) + C, where C is a constant of integration. Taking the derivative of the arc length with respect to time, we find that ds(t)/dt = 18√(1 + 4t^2) + 36t^2/√(1 + 4t^2). The derivative of the velocity vector with respect to arc length is then given by dv(t)/ds(t) = (18i + 36tj) / (18√(1 + 4t^2) + 36t^2/√(1 + 4t^2)). Simplifying this expression, we find that the normal component of the acceleration vector is a_n(t) = 18i / √(1 + 4t^2). Therefore, the normal component of the acceleration vector is 18i / √(1 + 4t^2).

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Answer:

B

Step-by-step explanation:

Answer:

B. \(\frac{x^2}{3^2} +\frac{y^3}{2^2} =1\)

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Interest rate risk is the risk that a fall in interest rate would decrease the value of a fixed rate investment. e.g. bonds , real estate.

Interest rate dropped 3 months after the house was bought. Robert is facing interest rate risk

Income risk is the risk that the stream of income received from a particular investment would drop as a result of a fall in interest rate.

Inflation risk is the risk that inflation would decrease the value of an investment

Answer:

b

Step-by-step explanation:

The probability that calls to exactly two randomly selected households will both go unanswered is 0.1849

From the question, we have the following parameters that can be used in our computation:

Probabiity of answering, p = 57%

This means that the probability that no one answers the call is

q = 1 - 57%

Evaluate

q = 43%

So, the probability that both calls will go unanswered is

P = q²

This gives

P = (43%)²

Evaluate

P = 0.1849

Hence, the probability is 0.1849

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The equivalent value of the expression -7 + 3(-4e⁻³) will be negative 7.597.

The equivalent is the expression that is in different forms but is equal to the same value.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ -7 + 3(-4e⁻³)

Simplify the expression, then we have

⇒ -7 + 3(-4e⁻³)

⇒ -7 - 12 / e³

⇒ -7 - -0.597

⇒ -7.597

The equivalent value of the expression -7 + 3(-4e⁻³) will be negative 7.597.

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so after 2 seconds we get

so the answer is A

Answer:

Rectangles are sometimes squares.

Step-by-step explanation: