Write the equation of the line that passes through the points (-7,5) and (−7,−8). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.

Answer:

The answer is 132 square units

Step-by-step explanation:

Cutting the shape

we have two trapeziums

A=(area of small +Area of big)Trapezium

A=1/2(3+9)8 + 1/2(9+12)8

A=1/2×12×8 + 1/2×21×8

A=12×4 + 4×21

A=48+84

A=132 square units

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:

Step-by-step explanation:

there are 12 adults and 42 kids which in total cost $306

hope this helped

Answer:

Yes! The given quadrilateral represents Parallelogram.

Reason:  The given quadrilateral has opposite angles congruent.

Step-by-step explanation:

Given the quadrilateral with the angles

We know that the sum of the angles of a quadrilateral is 360.

so

118°+62°+118°+62° = 360°

Thus, the given figure is indeed a quadrilateral.

Now in order to determine whether the given quadrilateral is a parallelogram or not, we need to check whether the opposite angles are congruent or not.

If the angles opposite of each other will have the same measurement, then the quadrilateral will represent Parallelogram.

It is clear that the given quadrilateral has two pairs of equal opposite angles.

i.e. The angle 118° has the same opposite angle 118° and the angle 62° has the same opposite angle 62°.

Therefore, the given quadrilateral represents Parallelogram.

Hence,

Yes! the given quadrilateral represents Parallelogram.

Reason: The given quadrilateral has opposite angles congruent.

Answer:

5/9 of the marbles are red

Step-by-step explanation:

Of the 45 marbles, 20 are black, and the other 25 are red. So 25/45, or 5/9, of the marbles are red.

The number of Jim's model car is 48

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

Ratio of the number of model cars that Jim owns to the number of model cars Terrence owns is 8 : 6

This means that

Jim : Terrence = 8 : 6

Also from the question, we have

Terrence owns 36 models cars

This means that

Terrence = 36

Substitute the known values in the above equation, so, we have the following representation

Jim : 36 = 8 : 6

Multiply by 6

Jim : 36 = 48 : 36

So, we have

Jim = 48

Hence, the number of car is 48

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The domain of the square root function is x greater-than-or-equal-to 0, since the function is defined for all non-negative x-values or x-values greater than or equal to zero.

The domain of the square root function graphed below can be determined by looking at the x-values of the points on the graph.

From the given information, we can see that the curve starts at (0, -1) and goes through (1, -2) and (4, -3).

The x-values of these points are 0, 1, and 4.

Since the square root function is defined for any non-negative x-values or x-values more than or equal to zero, its domain is x greater-than-or-equal-to 0.

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The area of the square is given as 100 square unit

You should be aware that the square has all its sides equal

The perpendicular from opposite vertices represent distance

The given vertices are

(2,2) and (10,8)

Using the formula for distance between two points

d=√(10-2)²+(8-2)²

d=√8²+6²

d = √64+36

d=√100

This implies that d=10

The area of a square is given as s²

Area = 10²

Atrea = 100 square units

In conclusion, the area of the square is 100 square units

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Translated question:

The vertices of a square ABCD are A(2,2) and B(10,8), Find the area of the square

A geometric shapes that can be used to create a logo that will fit in a measuring 15 cm by 15 cm is to use a square.

It should be noted that geometric shapes are the figure of area that is closed by a boundary.

In this case, a geometric shapes that. an be used to create a logo that will fit in a measuring 15 cm by 15 cm is to use a square.

This is because all the sides in a square are equal.

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Answer:

\(A = 25\pi\)  or  25 × 3.14 = 78.5m

Step-by-step explanation:

The radius is half of the diameter. So the radius = 5m  (10/2)

\(A = \pi r^{2}\)

\(A = \pi (5^{2} )\)

\(A = 25\pi\)

The  equation of the parabola with the following properties y = (-1/4)(x+3)^2 -1

To find the equation of a parabola, we can use the formula f(x) = ax^2 + bx + c, where a, b and c are congruent vertices.

Alternatively, we can use PF = PM to find the equation of the parabola.

vertex is half way between the focus and directrix

It's a downward opening parabola, general form

y= a(x-h)^2 + k

where (h,k) = vertex= (-3,-1)

plug in another point on the parabola to solve for a which gives

am answer with either x coefficient = -1'/4 or =4 Check the math.

one or the other is right another point is the y intercept = 9a-1

Another point is directly to the right of the focus  (-1, -2)  It's 2 down from the directrix and 2 to the right of the focus, equidistant.   plug that point into y= a(x+3)^2 -1 and solve for "a"  

-2 = a((-1+3)^2 -1

-2 = 4a -1

4a = -

a = -1/4

The parabola is y = (-1/4)(x+3)^2 -1

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Answer:

I haven't done that type of math in a while but I cam up with 21 bookmarks

Answer:

\((-1)+(-3)=-4\)

Step-by-step explanation:

We were originally on -1.

But we jumped to -4.

-4 is 3 spaces to the left of -1.

In other words, we subtract 3 into -1.

Another way of saying this is that we added -3 to -1.

Therefore, our equation is:

\((-1)+(-3)=-4\)

Answer:

a c

Step-by-step explanation:

The value of x obtained using the inverse trigonometric ratios for tangent  is x ≈ 51.1°

The tangent of an angle, θ, tan(θ) in a right triangle is the ratio of the length of the side adjacent to the angle to the length of the side opposite to the angle.

Mathematically; tan(θ) = Opposite/Adjacent

The details in the question includes;

The shape of the figure = A right triangle

The length of the side adjacent to the angle, ON x = 7.5

Length of the side opposite to the angle, NM x = 9.3

The measure of the angle x° can be found using the trigonometric ratio for tangent as follows;

tan(x) = NM/ON

Therefore;

tan(x) = 9.3/7.5

x° = arctan(9.3/7.5) ≈ 51.1°

x ≈ 51.1°

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SOLUTION

Given the question in the question tab, the following are the steps to find the equation

Step 1: Write the equation of the initial line and get the slope by comparing with the general line equation.

Step 2: Get the slope of the perpendicular line

The slopes of two perpendicular lines are negative reciprocals of each other. This means that if a line is perpendicular to a line that has slope m, then the slope of the line is -1/m.

Step 3: Get the y-intercept of the perpendicular line using the general equation of a line

Step 4: We compute the final equation of the line perpendicular to y=4/3x+1 through point (-7,-2)​

Hence, the equation of the line perpendicular to y=4/3x+1 through point (-7,-2)​ is:

Answer:

each ticket is $8.75

Step-by-step explanation:

c=8$8.75

The equation that can be used to determine the cost of each movie ticket is C = $48.50 / 6.

Total cost of the 6 movie tickets = (6 x cost of each ticket) - value of one coupon

50.50 = 6C - $2

Combine similar terms

$50.50 - $2 = 6C

$48.50 = 6C

Divide both sides of the equawtion by 6

C = $48.50 / 6

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Answer:

$815.63

Step-by-step explanation:

Commission=10875(.075)

                    =815.625

Answer:

A should be the answer

Step-by-step explanation:

Answer:

12/20

Step-by-step explanation:

\(\displaystyle \frac{3}{5}=\frac{3}{5}\cdot\frac{4}{4}=\frac{12}{20}\)

The answer is:

In-depth-explanation:

The denominator of 3/5 is 5. To get from 5 to 20, we multiply it by 4.

We need to multiply both the numerator and the denominator by 4, so we do this:

\(\sf{\dfrac{3\times4}{5\times4}}\)

\(\sf{\dfrac{12}{20}}\)

Answer:

=2745

Step-by-step explanation:

=2700+23−44+66

=2723−44+66

=2679+66

=2745

Answer:

Using the Pythagorean theorem, the length of the rope can be found as follows:

c^2 = a^2 + b^2

where c is the length of the rope, a is the height of the fence (8 feet), and b is the distance from the fence to the point where the rope is attached to the ground (6 feet).

Plugging in the values, we get:

c^2 = 8^2 + 6^2

c^2 = 64 + 36

c^2 = 100

c = √100

c = 10

Therefore, the length of the rope is 10 feet.

Answer:

The length of the rope is 10 feet.

Step-by-step explanation:

To find the length of the rope attached to the top of an 8-foot-tall fence and fastened to the ground 6 feet away, we can use the Pythagorean theorem, which states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. In this case, the vertical leg is the height of the fence (8 feet) and the horizontal leg is the distance from the base of the fence to where the rope is fastened (6 feet). Therefore, the length of the rope (the hypotenuse) is given by:

hypotenuse^2 = vertical leg^2 + horizontal leg^2

Substituting the values, we get:

hypotenuse^2 = 8^2 + 6^2

hypotenuse^2 = 64 + 36

hypotenuse^2 = 100

Taking the square root of both sides, we get:

hypotenuse = 10

So the length of the rope is 10 feet.

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Answer:

A, C, and D

Could you please give me Brainliest?

Answer:

answers are a c d

Step-by-step explanation:

look at the lines that' how you find your answer

Using the binomial distribution, the probabilities are given as follows:

a. None: 0%.

b.

c. The expected number of restaurants that will exceed the cost covered by your company is of 7.67.

Using the normal approximation, the probabilities are:

a. None: 0.0008 = 0.08%.

b.

The difference in these probabilities is due to the small sample size.

The formula for the probability of x successes is:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

In which the parameters are given by:

Considering that you will eat dinner at 23 restaurants, and at around one-third of them the meal cost will exceed 50 dollars, the values of these parameters are given as follows:

n = 23, p = 1/3 = 0.3333.

The probability that none will exceed is P(X = 0), hence:

P(X = 0) = (1 - 0.3333)^23 = 0% (rounded).

The probability of at most 12 is:

P(X <= 12) = P(X = 0) + P(X = 1) + ... + P(X = 12).

Using a binomial distribution calculator with the given parameters, the probability is:

P(X <= 12) = 0.9814 = 98.14%.

The probability that between 4 and 8 dinners are paid is:

P(4 <= X <= 8) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)

Using a calculator, or the mass function P(X = x) and adding each probability, the desired probability is:

P(4 <= X <= 8) = 0.0493 + 0.0937 + 0.1405 + 0.1707 + 0.1707 = 0.6249 = 62.49%.

The first step for the normal approximation is finding the mean and the standard deviation, as follows:

The probability of none, using continuity correction, is P(X < 0.5), which is the p-value of Z when X = 0.5, hence:

(the p-value of Z is found using the z-score table).

\(Z = \frac{X - \mu}{\sigma}\) (z-score formula)

Z = (0.5 - 7.67)/2.26

Z = -3.17

Z = -3.17 has a p-value of 0.0008.

Hence the probability is 0.0008 = 0.08%.

The probability of at most 12 is P(X <= 12.5), using continuity correction, which is the p-value of Z when X = 12.5, hence:

\(Z = \frac{X - \mu}{\sigma}\)

Z = (12.5 - 7.67)/2.26

Z = 2.14

Z = 2.14 has a p-value of 0.9838.

Hence the probability is of 98.38 = 98.38%.

The probability of between 4 and 8 dinners being paid is P(3.5 <= X <= 8.5), which is the p-value of Z when X = 8.5 subtracted by the p-value of Z when X = 3.5, hence:

X = 8.5:

\(Z = \frac{X - \mu}{\sigma}\)

Z = (8.5 - 7.67)/2.26

Z = 0.37

Z = 0.37 has a p-value of 0.6443.

X = 3.5:

\(Z = \frac{X - \mu}{\sigma}\)

Z = (3.5 - 7.67)/2.26

Z = -1.85

Z = -1.85 has a p-value of 0.0322.

Hence the probability is:

0.6443 - 0.0322 = 0.6121 = 61.21%.

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Answer:

160 inches

Step-by-step explanation:

47+33+47+33=160inches

Answer:

counted 27 raisins. If

there were 12

Answer: As we know that the formula of outlier is

IQR = Q3 - Q1

= 52 - 32

= 20

52 + 1.5(20) = 82...

so anything above 82 is an outlier

now

32 - 1.5(20) = 2.

..anything below 2 is an outlier

so...the 83 is outlier

so correct option is D

hope it helps

Step-by-step explanation:

Answer:

x = - 1

Step-by-step explanation:

( \(x_{1}\) , \(y_{1}\) )

( \(x_{2}\) , \(y_{2}\) )

m = \(\frac{y_{2} -y_{1} }{x_{2} -x_{1} }\)

~~~~~~~~~~~~~

Assume,

x = \(x_{1}\)

1 = \(y_{1}\)

- 3 = \(x_{2}\)

7 = \(y_{2}\)

m = - 3

then

\(\frac{7-1}{-3-x}\) = - 3

- 3 - x = 6 ÷ ( - 3 )

- 3 + 2 = x

x = - 1