What is the meaning of "ϕ(x, y, p)"?

Using the center and distance between co-vertex and center, the equation of the hyperbola is written below

[tex]\frac{(y + 3)^2}{49} - \frac{(x - 10)^2}{144} = 1[/tex]

A hyperbola, in analytic geometry, is a conic section that is formed when a plane intersects a double right circular cone at an angle such that both halves of the cone are intersected.

The equation of hyperbola is given as;

[tex]\frac{(y - k)^2}{a^2} - \frac{(x - h)^2}{b^2} = 1[/tex]

where (h,k) is the center of the hyperbola, a is the distance between a vertex and the center, and b is the distance between a co-vertex and the center.

In this case, the center is (10,−3), a=7, and b=12. Therefore, the equation of the hyperbola is

The equation of the hyperbola is;

[tex]\frac{(y + 3)^2}{49} - \frac{(x - 10)^2}{144} = 1[/tex]

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Answer:

Because y is a common variable, we can assume that they are equal to each other.

Answer:

tan T = 12/5

sin A = 12/13

sec Z = 97/65

m<H = 54.5°

Step-by-step explanation:

In general:

sin A = opp/hyp

cos A = adj/hyp

tan A = opp/adj

sec A = 1/cos A = hyp/adj

tan T = 48/20

tan T = 12/5

AB = √(100 + 576)

AB = 26

sin A = 24/26

sin A = 12/13

XZ = √(72² + 65²)

XZ = 97

sec Z = 97/65

tan H = 7/5

H = tan^-1 7/5

m<H = 54.5°

The line of symmetry from the graph of the absolute value function is given as follows:

x = 1.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

The line of symmetry for the absolute value function modeled above is given as follows:

x = h.

The coordinates of the vertex of the graphed linear function are given as follows:

(1, -1).

Hence the line of symmetry for the function graphed is given as follows:

x = 1.

This is because the x-coordinate of the vertex of the function is of x = 1.

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The height of a house that has a shadow projection of 2 meters is given as follows:

2.5 meters.

The height of a house that has a shadow projection of 2 meters is obtained applying the proportions in the context of the problem.

The proportional relationship between the height of the building and the height of the shadow is given as follows:

5/4 = x/2

Hence we apply cross multiplication to obtain the height of the house, as follows:

4x = 10

x = 10/4

x = 2.5.

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2x² -2x+2 is the  polynomial we obtained after subtraction

The given polynomials are (3x²-2x+5)-(x²+3)

Three times of x square minus two times of x plus five minus x square plus three

We have to subtract the polynomials

3x²-2x+5 -x² - 3

Combine the like terms

2x² -2x+2

Hence, the polynomial we obtained after subtraction is 2x² -2x+2

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The solution to the integration of the function given, ∫√(5x - 1) dx, is:

[tex]\frac{2}{15}(5x-1)^{3/2} + C[/tex]

To solve the integral of:

√(5x - 1) dx

we can use a u-substitution.

Let u = 5x - 1, then:

du = 5 dx

dx = du/5

Now we can rewrite the integral in terms of u:

∫√(5x - 1) dx = ∫√u * (du/5)

Simplifying the integral:

(1/5) ∫√u du

Integrating √u:

(1/5) * (2/3) * u^(3/2) + C

Where C is the constant of integration

Substituting back u = 5x - 1:

(2/15) * (5x - 1)^(3/2) + C

Therefore, the solution to the integral of √(5x - 1) dx is:

[tex]\frac{2}{15}(5x-1)^{3/2} + C[/tex]

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The ratios that are equivalent to the ratio 12:3 are 4:1 and 120:30.

We have,

To determine the ratios that are equivalent to the ratio 12:3, we need to find ratios that have the same value when simplified.

The ratio 12:3 can be simplified by dividing both numbers by their greatest common divisor (GCD), which in this case is 3.

Dividing 12 by 3 gives us 4, and dividing 3 by 3 gives us 1. Therefore, the simplified ratio is 4:1.

Now let's check the given options:

6:1 - This ratio is not equivalent because it is different from the simplified ratio 4:1.

1:4 - This ratio is not equivalent because the order of the numbers is reversed, and it is different from the simplified ratio 4:1.

4:1 - This ratio is equivalent to the original ratio 12:3. When simplified, both ratios result in 4:1.

246 - This is not a ratio and cannot be compared to the original ratio 12:3.

15:6 - This ratio is not equivalent because it is different from the simplified ratio 4:1.

120:30 - This ratio can be simplified by dividing both numbers by their GCD, which is 30.

Dividing 120 by 30 gives us 4, and dividing 30 by 30 gives us 1.

Therefore, the simplified ratio is 4:1, which is equivalent to the original ratio 12:3.

Thus,

The ratios that are equivalent to the ratio 12:3 are 4:1 and 120:30.

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In the given graph there is zero slope of the line.

As shown the points on the line

The coordinates of points be,

(4, 2) and (4, -2)

Since we know that slope of line passing through the points,

(x₁ , y₁) and (x₂, y₂) is, m = (y₂ - y₁)/(x₂ - x₁)

Here,

(x₁ , y₁) = (4, 2)

(x₂, y₂) = (4, -2)

Now the slope be = (-2 - 2)/(4 - 4)

                              = -4/∞

                              = 0

Therefore,

There is zero slope.

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The bisector angle is angle PQT which is equal to angle RQT.

Angle bisector or a bisector angle is a type of angle obtained after dividing the initial angle into two equal parts.

The bisected angle can be obtained using a pair of compass and a pencil attached to it.

To bisect the given angle RQP; we will take the following steps;

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The half of 11 5/8 inches is; 5 13/16

Half of a fraction

The number given is; 11 5/8 inches

This can be written as an improper fraction;

= ((8×11)+5)/8 = 93/8

Hence, half of 93/8 is;

= 93/8 ÷ 2

= 93/8 × 1/2

= 93/16

= 5 13/16

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The two figures are congruent because a reflection and a translation are used to map Figure 1 onto Figure 2.

The angle corresponding to angle M is given as follows: <S.

Examples of transformations are given as follows:

For this problem, the two transformations are:

These two are rigid motions, keeping the side lengths constant, hence the figures are congruent.

Angle S is corresponding to angle M, as they are the angles at the "pointed" vertex of the figure.

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The critical value to use in constructing the confidence interval is 1.645. This critical value corresponds to the 90% confidence level.

The critical value to be used in constructing the 90% confidence interval is 1.645. This is the z-score associated with a 90% confidence level. In other words, this is the value that is 1.645 standard deviations away from the mean. This value is found using the z-table, which contains the probability values for a standard normal distribution.

Therefore, the critical value to use in constructing the confidence interval is 1.645. This critical value corresponds to the 90% confidence level.

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There are a fixed number of trials is not a condition for a geometric setting

In a geometric setting, we are dealing with a sequence of independent trials, where each trial can result in either a success or a failure.

The key concept in a geometric setting is the number of trials needed until the first success occurs.

The trials are independent  is essential in a geometric setting.

It means that the outcome of one trial does not affect the outcome of subsequent trials.

The probability of success is the same for each trial is also crucial in a geometric setting.

It implies that the probability of achieving a success does not change from trial to trial.

There are a fixed number of trials is not specific to a geometric setting.

The variable of interest is the number of trials required to reach the first success is fundamental to a geometric setting.

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The volume of the two prisms compares that the volume of prism B will double.

We are given that side length of the cube measured 18 inches in length. She built another prism (Prism B) with the same dimensions as the cube, except she doubled its height.

When the prism is such that if we slice it horizontally at any height smaller or equal to its original height, the cross-section is same as its base, then its volume is:

V = B x h

So, the volume of the two prism A= V = B x h

V = 18 x h = 18h

the volume of the two prism B= V = B x h

V = 18 x 2h = 36h

So, the volume of prism B will double thus the correct option is B.

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The complete question is;

Anna built a prism (Prism A) out of a cube of wood. The side length of the cube measured 18 inches in length. Anna built another prism (Prism B) with the same dimensions as the cube, except she doubled its height.

How does the volume of the two prisms compare?

The volume of prism B will triple.

The volume of prism B will double.

The volume of prism B will decrease.

The volume of prism B will be cut in half.

Based on the information, it should be noted that the value of tan(A-B) is 234/583.

Given:

tanA = 60/11

sinB = 45/53

A and B are in Quadrant I

We can use the following identity to find tan(A-B):

tan(A-B) = (tanA - tanB)/(1 + tanA*tanB)

Substituting the given values, we get:

tan(A-B) = (60/11 - 45/53)/(1 + (60/11)*(45/53))

= (15/53)/(295/583)

= 234/583

Therefore, the value of tan(A-B) is 234/583.

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The volume of the hexagonal prism is 212.4 unit square

Prism is three-dimensional solid which has identical faces at both ends. It is a polyhedron, which means all faces are flat.

How to determine this

When an hexagonal prism has a base area = 36 units

Height = 5.9 units

Volume of Prism = Base area * Height

Volume of prism = 36 units * 5.9 units

Volume = 212.4 units square

Therefore, the volume of the hexagonal prism is 212.4 units square

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Answer:

sin(3pi/4 ) = -√2/2

So, B.

Answer:

hello

the answer is:

f = 180 - 42 - 90 = 48

The solutions for the quadratic graph are (d) (-3, 0) and (1, 0)

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

The quadratic graph

The solutions for the quadratic graph are the points where the graph intersect the x-axis

These points are called the x-intercepts or the roots

Using the above as a guide, we have the following:

The point of intersection with the x-axis are (-3, 0) and (1, 0)

Hence, the solutions for the quadratic graph are (d) (-3, 0) and (1, 0)

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Answer: 150 deg

Step-by-step explanation:

cosine is negative in quadrants 2 and 3. the current angle, 210, is in quad 3. It will have an equal cosine value in quad 2.

that angle will be -210 degrees. in positive terms that is 360-210 = 150 degrees.

thus the answer which shows 150 degrees is correct.

in general:

[tex]cos(x) = cos(-x)[/tex]

Answer:

n = 10

Step-by-step explanation:

Factorial is denoted by an exclamation mark "!" placed after the number. It means to multiply all whole numbers from the given number down to 1.

Therefore, n! represents the product of all positive integers from 1 to n.

[tex]\boxed{n!=n \times(n-1) \times(n-2) \times ... \times 1}[/tex]

Given expression:

[tex]n! = (2^8)(3^4)(5^2)(7)[/tex]

The expression for n! has been given as the product of prime factors.

As n! represents the product of all positive integers from 1 to n, begin by writing out the positive integers from 1 in ascending order as the product of primes (using exponents where possible):

[tex]\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}\cline{1-14}\vphantom{\dfrac12}n&1&2&3&4&5&6&7&8&9&10&11&12&13\\\cline{1-14}\vphantom{\dfrac12}\sf Product\;of\;primes&1&2&3&2^2&5&3\cdot 2&7&2^3&3^2&5 \cdot 2&11&2^2\cdot 3&13\\\cline{1-14}\end{aligned}\;\;\sf etc.[/tex]

If we examine the prime products of the given expression, we can see that largest prime number 7 appears only once. Therefore, n must be less than 14, since the next time 7 appears as a prime factor is when 2 · 7 = 14.

The prime number 5 appears twice in the given expression.

From the above table, we can see that the first two times the number 5 is present is (1) on its own, and (2) as a factor of 10. Therefore, n must be equal to or more than 10.

The prime number 3 appears four times in the given expression.

From the above table, we can see that the first four times the number 3 is present is (1) on its own, (2) as a factor of 6, (3) & (4) as both factors of 9.

The 5th time prime number 3 is present is as a prime factor of 12. Therefore, n must be less than 12, else 2⁵ would be a factor of n!.

Therefore, we have determined that 10 ≤ n < 12.

As 11 is a prime number and does not appear in the given expression for n!, we can conclude that n = 10.

We can check this by calculating the given expression and 10!:

[tex]\begin{aligned}n! &= (2^8)(3^4)(5^2)(7)\\&=256 \cdot 81\cdot25\cdot7\\&=20738\cdot25\cdot7\\&=518400\cdot7\\&=3628800\end{aligned}[/tex]

[tex]\begin{aligned}10!&=10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=90 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=720 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=5040 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=30240 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=151200 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=604800 \cdot 3 \cdot 2 \cdot 1\\&=1814400 \cdot 2 \cdot 1\\&=3628800 \cdot 1\\&=3628800\end{aligned}[/tex]

Therefore, this proves that n = 10.

Answer:

12 cm ^2

Step-by-step explanation:

Using the formula

V=ABh

Solving forAB

AB=V

h=204

17=12cm²

Answer:

2/3=10/15

3/5=9/15

Step-by-step explanation:

In order to turn 2/3 and 3/5 using 15 as the common denominator, we must first find out how much we need to multiply the denominator by to get 15 and use that amount to also multiply the numerator. In 2/3 the 3 needs to be multiplied by 5, therefore we also multiply the 2 by 5 giving us the result of 10/15 for the 2/3 problem. For the 3/5 we use the same tactic. The 5 in 3/5 needs to be multiplied by 3 to get to 15, therefore we multiply the 3 by 3 as well to get 9/15.

Since AC is the angle bisector of ∠BAD, the flowchart proof should be completed as follows;

Statement                                 Reason

AC bisects ∠BAD                      Given

∠BAC ≅ ∠DAC                         Definition of an angle bisector.

∠BCA ≅ ∠DCA                         Congruent angles of a triangle (SAS).

AC ≅ AC                                   Reflexive property

ΔABC ≅ ΔADC                         AAS postulate

In Mathematics and Geometry, an angle bisector can be defined as a type of line, ray, or segment, that typically bisects or divides a line segment exactly into two (2) equal and congruent angles.

By applying the angle bisector theorem to the given triangle, we have the following statements and justifications:

AC bisects ∠BAD       Given

∠BAC ≅ ∠DAC           Definition of an angle bisector.

Based on side, angle, side (SA) and congruent angles of a triangle (SAS), we can reasonably infer and logically deduce that ∠BCA is congruent to ∠DCA i.e ∠BCA ≅ ∠DCA.

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A point on circle B with integer coordinates when r = 1 would be (5, 6).

We have, the radius of Circle A is 6 unit.

and, Radius of Circle B= 6/2= 3 unit

Using the center (2, 3) and the radius 3, we can calculate the coordinates of a point on circle B as follows:

x-coordinate = center x-coordinate + radius = 2 + 3 = 5

y-coordinate = center y-coordinate + radius = 3 + 3 = 6

So, a point on circle B with integer coordinates when r = 1 would be (5, 6).

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Answer:

Unlikely.

Step-by-step explanation:

Possibility Formula: [tex]\frac{Desired Outcome}{Total Possible Outcoes}[/tex]

We want to roll a 5. On a standard six-sided die, then the odds of that happening is [tex]\frac{1}{6}[/tex]

[tex]\frac{1}{6}[/tex] is unlikely.