These 3 points are on a parabola defining the edge of a ski:

(-4,1)
(-2,0.94)
(0,1)
The general form for the equation of a parabola is .


1.
Use the x- and y-values of 1 to build a linear equation with 3 variables: A, B, and C.
Repeat this process with the other 2 points to build a 2nd linear equation.
Record all three equations in the box below.

2.
Build a matrix equation that represents this system of equations. Record your matrix equation here.

3.
Use a graphing calculator or other graphing utility to find the inverse of the coefficient matrix. Record your result here.

4.
Use the inverse matrix to solve the system of equations. Record the equation of the parabola here.

The first step is to locate the points to find what kind of quadrilateral this is.

The next step is to find the lengths of the diagonals, if both have the same length then the quadrilateral is a rectangle, if the don't the quadrilateral is a parallelogram.

When looking at the picture is easy to determine that the quadrilateral is a parallelogram, but the statement that could prove what kind of quadrilateral this is is C. Find the lengths of the diagonals to show that the quadrilateral is a parallelogram.

Answer: 8

Step-by-step explanation:

Substitute the given value into the function and evaluate.

Explanation:

Replace n with 100 and simplify

f(n) = 9n-1

f(100) = 9(100)-1

f(100) = 900-1

f(100) = 899

The 100th term is 899

The solutions to the given quadratic equation are x=11 and x=-3.

The given quadratic equation is x²-8x-33=0.

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

By using splitting middle term method, we get

x²-11x+3x-33=0

x(x-11)+3(x-11)=0

(x-11)(x+3)=0

(x-11)=0 and (x+3)=0

x=11 and x=-3

Therefore, the solutions to the given quadratic equation are x=11 and x=-3.

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The probability that a mouse leaves first and then a bat is given as follows:

14/55.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

As the animal is not replaced, the probabilities for this problem are given as follows:

Hence the probability is given as follows:

4/11 x 7/10 = 2/11 x 7/5 = 14/55.

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The answer is 0.360, or approximately 36/100.

Probability can be defined as the ratio of number of favourable outcomes and total number of outcomes.

The probability of matching four out of six numbers in a single ticket can be calculated as follows:

There are C(23, 6) = 8,145 possible combinations of six numbers from 1 through 23.

There are C(23, 4) = 1,531 possible combinations of four numbers from 1 through 23.

So, the probability of matching four out of six numbers in a single ticket is 1,531/8,145 = 19/102.

If you buy five tickets, the probability of matching four out of six numbers in at least one of them is 1 - (1 - 19/102)⁵ , which can be calculated as:

1 - (1 - 19/102)⁵ = 1 - 0.848⁵ = 1 - 0.640 = 0.360

Therefore, The answer is 0.360, or approximately 36/100.

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Answer:

820

Step-by-step explanation:

Find the number in the ten place 2 and look one place to the right for the rounding digit 3. Round up if this number is greater than or equal to

5 and round down if it is less than 5.

The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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Answer:

(7,12),(-12,-7)

Step-by-step explanation:

x^2 + y^2 = 193

x - y = - 5

x = y - 5

(y - 5)^2 + y^2 = 193

y^2 - 10y + 25 + y^2 = 193

2y^2 - 10y + 25 = 193

2y^2 - 10y + 25 - 193 = 0

2y^2 - 10y - 168 = 0

2*(y^2 - 5y - 84) = 0     This factors into

2*( y - 12) (y + 7) = 0

y = 12    

in which case x = 12 - 5 = 7

y = - 7

in which case x = -7 - 5 = - 12

Answer: The lines below are perpendicular.

Step-by-step explanation: They are perpendicular because they start at one side and end at the side across.        Hope this helped!!! :)

The measure of angle MTU m∠MTU is 114 degree.

From the figure in the diagram:

Measure of angle STU is 145 degrees and measure of angle STM is 31 degree.

Since, angle STU composes or is the sum of angle STM and angle MTU.

To find angle MTU, simply subract angle STM from angle STU.

m∠STU = m∠STM + m∠MTU

Hence:

m∠MTU = m∠STU - m∠STM

Plug in the given values and simplify

m∠MTU = 145° - 31°

Subtract 31 from 145

m∠MTU = 114°

Therefore, angle MTU measure 114°.

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Answer:

slope (m) = 2/3

Step-by-step explanation:

slope = change in x /change in y

Also, slope is y2 - y1 / x2 -x1. That is what I apply for this activity, hence:

slope = 3 - (-1) / 0 - (-6)

         = 3 + 1 / 0 + 6

         = 4 / 6

         = 2/3

∴ slope(m) = 2/3

Answer:

19.6, B

Step-by-step explanation:

To solve, we need to figure out how many gallons of white paint she needs for every gallon of brown paint.

We are given this equation.

5 gallons of brown paint = 7 gallons of white paint

Divide both sides by 5.

1 gallon of brown paint = 7/5 gallons of white paint = 1.4 gallons of white paint

Now, using this, substitute 14 into the left side.

14 gallons of brown paint = 1.4 * 14 gallons of white paint

14 gallons of brown paint = 19.6 gallons of white paint

Thus, the answer is B, 19.6 gallons

Answer:

(a) 16 students failed for exactly two of the three reasons.

(b) 7 students failed because of poor attendance and not studying but not because of not turning in assignments.

(c) 14 students failed because of exactly one of the three reasons.

(d) 3 students failed because of poor attendance and not turning in assignments but not because of not studying.

Step-by-step explanation:

We are given that one semester in a chemistry class, 14 students failed due to poor attendance, 23 failed due to not studying, 15 failed because they did not turn in assignments, 9 failed because of poor attendance and not studying, 8 failed because of not studying and not turning in assignments, 5 failed because of poor attendance and not turning in assignments, and 2 failed because of all three of these reasons.

As shown in the diagram attached below, a Venn diagram represents the situation given in the question;

In the diagram below, 2 in represents purple color represents the number of students failed because of all three of these reasons.

7 represents the number of students who failed because of poor attendance and not studying but not due to not turning in assignments.

6 represents the number of students who failed because of not studying and not turning in assignments but not due to poor attendance.

3 represents the number of students who failed because of poor attendance and not turning in assignments but not due to not studying.

2 in red color represents the number of students who failed only due to poor attendance.

8 in red color represents the number of students who failed only due to not studying.

4 in red color represents the number of students who failed only due to not turning in assignments.

(a) The number of students who failed because of exactly two of the three reasons = 7 + 6 + 3 = 16 students.

(b) The number of students who failed because of poor attendance and not studying but not because of not turning in assignments = 9 - 2 = 7 students.

(c) The number of students who failed because of exactly one of the three reasons = 2 + 8 + 4 = 14 students.

(d) The number of students who failed because of poor attendance and not turning in assignments but not because of not studying = 5 - 2 = 3 students.

Answer:

$9.24 for 12 lbs.

Step-by-step explanation:

To solve, divide the cost with the amount of pounds you get:

$4.80 for 5 lbs:

Divide 4.80 with 5:

4.80/5 = 0.96

If you were to buy 5 lbs for $4.80, each pound will cost $0.96.

$9.24 for 12 lbs:

Divide 9.24 with 12:

9.24/12 = 0.77

If you were to buy 12 lbs for $9.24, each pound will cost $0.77.

∴ Purchasing 12 lbs of flour for $9.24 will be cheaper by $0.19 per pound.

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The Venn diagram for (D ⋃ E) ⋃ F will be the ovarlapped region of D,E and F.

To represent the sets D, E, and F in the Venn diagram, we first construct three overlapping circles. Then, beginning with the innermost operation and moving outward, we shade the regions corresponding to the set operations in the expression.

We shade the area where the circles for D and E overlap because the equation (D ⋃ E)  denotes the union of the sets D and E. All the elements in D, E, or both are represented by this area.

The union of (D ⋃ E) with F is the next step. This indicates that we darken the area where the circle for F crosses over into the area that we shaded earlier. All the components found in sets D, E, F, or any combination of these sets are represented in this region.

The final Venn diagram should include three overlapping circles, with (D ⋃ E) ⋃ F shaded in the area where all three circles overlap.

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Answer:

6(72)= 432 & 8(74.25)=594

594-432=162==> 162-80=82

Answer:

125

Step-by-step explanation:

90+145=235

360-235=125

Answer:

x=35

Step-by-step explanation:

Because with two angles making up one side of a straight line like that, their total will always be 280 degrees, Seein g that one of the angles is 145. 180-145= x or 35

Answer:

8

Step-by-step explanation:

4x8 =32

Answer:

8

Step-by-step explanation:

32 ÷ 4 = 8

or

4 × 8 = 32

there were so many solutions

Answer:

x = -3/2

Step-by-step explanation:

Let's solve your equation step-by-step.

4(x+2(3x−7))=22x−65

Step 1: Simplify both sides of the equation.

4(x+2(3x−7))=22x−65

(4)(x)+(4)(2(3x−7))=22x+−65(Distribute)

4x+24x+−56=22x+−65

(4x+24x)+(−56)=22x−65(Combine Like Terms)

28x+−56=22x−65

28x−56=22x−65

Step 2: Subtract 22x from both sides.

28x−56−22x=22x−65−22x

6x−56=−65

Step 3: Add 56 to both sides.

6x−56+56=−65+56

6x=−9

Step 4: Divide both sides by 6.

6x = -9

6       6

x =  -3/2

After the second stop, there are 10 fewer people on the bus compared to the number of people on the bus before the 2:30 stop.

Before the 2:30 stop, the bus let off 15 people and let on 9 people. The total change in the number of people at that stop is -15 (let off) + 9 (let on) = -6.

Therefore, there are 6 fewer people on the bus after the 2:30 stop compared to before that stop.

Ten minutes later, the bus makes another stop and lets off 4 more people. This additional change needs to be considered.

Since the previous calculation only accounted for the changes up until the 2:30 stop, we need to adjust the total change by including the subsequent stop.

Adding the change of -4 (let off) to the previous total change of -6, we get a new total change of -10.

Therefore, after the second stop, there are 10 fewer people on the bus compared to the number of people on the bus before the 2:30 stop.

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Answer: k = 76 degrees

Step-by-step explanation:

A linear pair of angles are always supplementary. (They sum to 180)

If the pair of angles are k and 104, they have to add up to equal 180.

180-104= 76

K has to equal 76 degrees

Answer:

B. 76

Step-by-step explanation:

I just took the quiz and got it right

Ahem, here goes, my attempt at a minute-long rap in praise of the parallelogram:

Yo, listen up, the parallelogram is where it's at,

A shape so brilliant, the angles are sat.

Parallel sides that never converge,

Internal angles that never diverge.

Each side an equal length,

A geometry prodigy's dream length.

The diagonals intersect, another line through the middle they meet,

Creating symmetry so neat.

A rectangle it could be,

But it's oblong, not square, can't you see?

With depth and width in perfect balance we see,

A two-dimensional form of complexity.

While the square is simple, the parallelogram is hip,

A mathematical masterpiece, skip, skip, skip!

four right angles keep the shape so tight,

Parallel lines dominate left and right.

Rotated or reflected without a care,

Its structural integrity beyond compare.

triangles form at each corner you'll note,

Acute or obtuse, depends on the protractor's groove.

A versatile shape with reason and purpose galore,

The parallelogram, simply, carries the floor.

From geometry to art, its angles they intrigue,

As a basis for patterns, its potential we can truly plug.

A forgotten form that deserves more acclaim,

Put the parallelogram on geometry's game!

This shape so underrated, rarely appreciated it seems,

But with logic and virtue, strong foundations it gleams.

The parallelogram, the parallelogram, Hooray!

This is why the parallelogram is the best shape, I say!

Answer:

3

Step-by-step explanation:

1. 54÷6 =9

2. (12-4)=8

3. 9-8 = 1

4. 1+2 = 3

5. I hope this helps it's pretty simple oh and 3 is your anansw.Also you can you your calculator

Answer:

a=72\(\frac{2}{3}\)

Step-by-step explanation:

56/6*(12-4)+2=n

56/6*8+2-2=n-2

56/6*8/8=(n-2)/8

x=9\(\frac{1}{3}\)

x=(n-2)/8

y=74\(\frac{2}{3}\)

y=n-2=a

a=72\(\frac{2}{3}\)

Answer:

Step-by-step explanation:

When naming lines, you can use the label of the line, in this case, m, and can also name the points in either direction, since the line goes on forever in both directions (it's different with rays). The leaves only line B as an answer.

The vertex of XYZ would be Y, since the vertex is always the middle number.

The hyperbola (y + 3)²/9 − (x − 2)²/2 = 1 has a center of (2, -3)

This is a pair that is formed when planes intersect

The equation of the hyperbola is given as

(y + 3)²/9 − (x − 2)²/2 = 1

The formula of a hyperbola is represented as

(y - k)²/a² − (x − h)²/b² = 1

Where the center is (a, b) and the lengths of the axes are variables a and b

Also, we have:

The coordinates of the center of the hyperbola is

Center = (h, k)

Next, we compare the equations

(y - k)²/a² − (x − h)²/b² = 1 and (y + 3)²/9 − (x − 2)²/2 = 1

From the comparison, we have

(h, k) = (2, -3)

This means that the center is (2, -3)

Hence, the coordinates of the center are (2, -3)

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The simplification of the given expression after addition = 130.

Addition is defined as one of the arithmetic operations that is used for the combination of two of more values.

The given values from the question above;

67 + 63 = 130

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Answer:

3/4

Step-by-step explanation:

Ok, so I see that the x-intercept is (4,0), while the y-intercept is(-3,0)

Slope is rise/run

Between these two points, the line rose 3 and horizontally went 4 units to the right. Therefore, the slope is 3/4.

Feel free to tell me if I did anything wrong! :)

Also, if you're still confused, I could explain it another way.