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How many solutions does this system of equations have?
y= -6x-7
y=-6x-7

( a)ρ² = (5/6) sec² θ.

(b) ρ = ±√(5 - 5 cos² θ) / sin θ cos φ.

For part (a) 6z² = 5x² + 5y²

The spherical coordinates for the variables x, y, and z are as follows:

x = ρsinθcosφy = ρsinθsinφz = ρcosθ

Substitute the values of x, y, and z into the given equation:6 (ρ cos θ)² = 5(ρ sin θ cos φ)² + 5(ρ sin θ sin φ)²

Simplify:6ρ² cos² θ = 5ρ² sin² θ (cos² φ + sin² φ)6ρ² cos² θ = 5ρ² sin² θ

Substitute sin² θ = 1 - cos² θ:6ρ² cos² θ = 5ρ² (1 - cos² θ)6ρ² cos² θ = 5ρ² - 5ρ² cos² θ6ρ² cos² θ + 5ρ² cos² θ = 5ρ²6ρ² = 5ρ² / (cos² θ + 5cos² θ)6ρ² = 5ρ² / cos² θ(6/5)ρ² = sec² θρ² = (5/6)sec² θ

The equation in spherical coordinates is ρ² = (5/6) sec² θ.

For part (b) x² + 5z² = 5

The spherical coordinates for the variables x, y, and z are as follows:

x = ρsinθcosφy = ρsinθsinφz = ρcosθ

Substitute the values of x, y, and z into the given equation:

(ρsinθcosφ)² + 5 (ρ cosθ)² = 5ρ²ρ² sin² θ cos² φ + 5 ρ² cos² θ = 5ρ²

Rearrange:ρ² (sin² θ cos² φ + 5 cos² θ - 5) = 0sin² θ cos² φ + 5 cos² θ - 5 = 0sin² θ cos² φ = 5 - 5 cos² θsin θ cos φ = ±√(5 - 5 cos² θ)

The equation in spherical coordinates is ρ = ±√(5 - 5 cos² θ) / sin θ cos φ.

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The remaining side is 16.9 and remaining angles are 83.1 and 34.9.

The cosine formula to find the side of the triangle is given by:

c = √[a² + b² – 2ab cos C] Where a,b and c are the sides of the triangle.

Given:

m∠B = 62°, a = 11, and c = 19

Now, b² = a² + c² - 2ac cos B.

b = √ a² + c² - 2ac cos B

b = √ 11² + 19² - 2x 11  x 19 cos 62

b= 16.9

Now. a/ sin A = b/ sin B= c/ sin C

So, <C = arc sin ( c sin B /b)

<C = arc sin ( 19 sin 62 /16.9)

<C = 83.1

and, <A = arc sin ( a sin B /b)

<A = arc sin ( 11 sin 62 /16.9)

<A = 34.9

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Answer:

Test each set of lengths using Pythagoras' Theorem. Is a2+b2=c2?

Step-by-step explanation:

Answer:

You have to see each one and do the formula, a^2*b^2= c^2, then under'root the c^2 to become c

The probability that the mean number of lightning strikes per square kilometer is less than 5 is 0.0016, when  open ground in a year has mean 6 and standard deviation 2.4.

It imply a quantity that falls somewhere between the values of the extreme members of a set in mathematics. There are different types of means, and how they are calculated relies on the relationship that is known about or is regarded as governing the other members.

Given,

Mean = 6

Standard deviation = 2.4

The value that has been reduced by the population mean and divided by the standard deviation is called the z-value.

z = x - mean/ standard deviation/√n

z = 5 - 6/2.4/√50

z = - 2.95

Using table A, calculate the corresponding probability;

= P(x <5)

= P( z < -2.95)

= 0.0016

The probability that the mean number of lightning strikes per square kilometer is less than 5 is 0.0016.

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The external auditor gathers a sample of shipping documents and matches them to entries in the sales journal to provide corroborating evidence that recorded sales represent authorized transactions.

This is because shipments of goods are recorded as sales, and shipments of goods are for authorized sales. Therefore, recorded sales were for goods that were shipped.In addition, it is essential to note that FOB (Free On Board) shipping point is a legal term that indicates that the buyer assumes ownership of the goods as soon as they leave the seller's dock. As a result, the buyer is responsible for paying for the transportation of the goods from the seller's location to their destination.

Therefore, when a rich company sells household goods and appropriately records its sales upon shipment, it indicates that the goods are shipped FOB (Free On Board) shipping point. This method is used to ensure that shipments of goods are for authorized sales and that recorded sales were for goods that were shipped.

The external auditor gathers a sample of shipping documents and matches them to entries in the sales journal to provide corroborating evidence that the recorded sales represent authorized transactions.

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Answer:

It has a maximum value of 30 and x occurs at x=3

Step-by-step explanation:

With where x occurs

\(x = \frac{ - b}{2a} \)

\(x = \frac{ - 18}{2( - 3)} \)

hence x occurs at x=3

with that of the maximum value

\( - ( \frac{b { }^{2} - 4 ac}{4a} )\)

hence

\( - ( \frac{( 18) {}^{2} -4(3)( - 3) }{4( - 3)} )\)

therefore the maximum value is 30

The number of ways to choose one red marble or one small marble will be 22.

When the order of the arrangements counts, a permutation is a numerical approach that establishes the total number of alternative arrangements in a collection.

The number of alternative configurations in a collection of things when the order of the selection is irrelevant is determined by combination.

As per the given,

Total number of red marbles = 8 + 5 = 13

Number of ways to choose on red marbles = 13

Total number of small marble = 5 + 4 = 9

Number of ways to choose on small marble = 9

One red or one small = 13 + 9 = 22

Hence "There are 22 different ways to select one red stone or one little marble".

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Answer: He got to be elected president of the Republic of Texas.

Answer:

(-5, 2)

Step-by-step explanation:

Three corners of a rectangular city block are located at (2,2), (2,-4) and (-5,-4) on a coordinate plane. What are the coordinates of the fourth Coordinate?

Solution:

A rectangle is a quadrilateral (has four sides and four angles) in which opposite sides are equal and parallel. Also, all the angles are at 90 degrees.

Since the city block is rectangular in shape, therefore the fourth coordinate would have the same y coordinate as the point (2, 2) and it would also have the same x coordinate as (-5, -4).

Hence the fourth coordinate is (-5, 2)

Answer:

The answer is B

Step-by-step explanation:

Hope it helps

Please give me the brainliest please!!! :[ I've never gotten one before.

Answer:

the mean of A and C is 10

Step-by-step explanation:

Given;

mean of A and B = 20

mean of B and C = 24

mean of A, B and C = 18

\(\frac{A + B}{2} = 20\\\\A+ B = 40 ---- (1)\\\\\frac{B + C}{2} = 24\\\\B+ C = 48----(2)\\\\\frac{A+ B+ C}{3} = 18\\\\A+ B+ C= 54---(3)\\\\From (1); \ A = 40 - B\\\\From(2); \ C = 48 - B\\\\\Substitute \ the \ values \ of \ A \ and \ C \ into \ (3)\\\\(40-B) + B + (48-B) = 54\\\\simplify;\\\\(40 + 48) + (B-B-B)= 54\\\\88 -B = 54\\\\-B = 54-88\\\\-B = -34\\\\B = 34\)

Recall; A = 40 - B

           A = 40 - 34

           A = 6

Also, C = 48 - B

        C = 48 - 34

       C = 14

Therefore, the mean of A and C is calculated as;

\(= \frac{A + C}{2} \\\\= \frac{6 + 14}{2} \\\\= 10\)

Answer:

√29

Step-by-step explanation:

We have points (3,4) and (5,9), so the distance:

Answer:

The actual answer is C

Step-by-step explanation:

The series (-3)+(-1)+3+9+...+97 to n terms can be expressed in sigma notation as: ∑_{k=1}ⁿ ((k-1) + 97(-1)\(^k\)).

The series starts with -3 and each term is obtained by multiplying the previous term by -1 and then adding 4 to it. We can express this recurrence relation using the formula:

a_{n+1} = -a_n + 4

where a_1 = -3.

To write this series in sigma notation, we can use the following formula:

∑_{k=1}ⁿ a_k = a_1 + a_2 + ... + a_n

Substituting the recurrence relation for a_k, we get:

∑_{k=1}ⁿ a_k = -3 + (-3+4) + (-(-3+4)+4) + ... + (-1)⁽ⁿ⁻¹⁾(-3+4) + (-1)ⁿ(97)

Simplifying this expression, we can factor out -3+4 from each term:

∑_{k=1}ⁿ a_k = (-3+4) + (-3+4) + (-3+4) + ... + (-3+4) + (-3+4) + 97(-1)ⁿ

There are n-1 terms of (-3+4), and the last term is 97(-1)ⁿ. Therefore, we can write:  

∑_{k=1}ⁿ a_k = (n-1)(-3+4) + 97(-1)ⁿ

Simplifying this expression, we get:

∑_{k=1}ⁿ a_k = (n-1) + 97(-1)ⁿ

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Answer:

a)1/12

b)3/4

c)5/12

d)2/3

Step-by-step explanation:

let chocolate bar be C

let fruit chew be F

let Pack of buble gum be =B

1let sour Candie be S

C=4

F=4

B=1 pack

S=3

T=4+4+1+3=12

a) 1/12

b)9/12=3/4

c)4/12+1/12=1/3+1/12=5/12

d)8/12=2/3

50.24 cm is the circumference, in centimeters, of the circle whose radius is 8cm. The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary.

The circumference of a circle is referred to as its perimeter. It is the entire circle's circumference. The diameter of a circle is multiplied by the constant to determine its circumference. For someone to cross a circular park or to enclose a circle, the diameter of the circle must be known. The length is measured in the same units as the diameter, which is a linear variable. An enclosed, circular form called a circle has border points that are all equally separated from the centre. Two essential metrics of a circle are its diameter and area.

As is common knowledge, the circumference of a circle is equal to twice its radius, or r.

Given: 8 cm is the circle's radius

Circumference of circle = 2 * 3.14 * 8 = 50.24 cm

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Correct question:

Taking π=3.14, find the circumference of a circle whose radius is 8cm.

The solution is 2 roots

The number of roots the equation will have if the value of the discriminant is 73 will be 2 roots

What is Quadratic Equation?

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the quadratic equation be A

where A = ax² + bx + c=0

Let the discriminant of the equation be D

Now , the value of D = 73

To calculate the number of roots a quadratic equation A

We need to compute the discriminant (b² - 4ac).

If the discriminant is less than 0, then the quadratic has no real roots.

If the discriminant is equal to zero then the quadratic has equal roots.

If the discriminant is more than zero then it has 2 distinct roots.

So , the value of D > 0

Therefore , the equation has 2 roots

Hence , the number of roots of the quadratic equation is 2 roots

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Answer: A

Step-by-step explanation:

The probability that the first three questions have the same answer choice is 1/4, since there are four answer choices and the instructor is randomly selecting the answers according to a discrete uniform distribution. This means that each answer choice has an equal probability of being chosen. Therefore, the probability of all three questions having the same answer is 1/4.

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Answer:

20.5

Step-by-step explanation:

hope it helps you that is all I could do.

Answer:

12

Step-by-step explanation:

let x = number of 3 wheel stollers

let y = number of 4 wheel strollers

x + y = 28

y = 28 - x

3x + 4y = 100

3x + 4(28 - x) = 100

3x + 112 - 4x = 100

-x = -12

x = 12

And there you go, your answer is 12.

Answer:

B

Step-by-step explanation:

12

The least number of seats the manger could order to 270 seats

The information that the the seats are sold only in groups of 10 will help to know that the order will be in a multiple of 10.

The manager wants to order 267 seats and this is not a multiple of 10 the nearest multiple of 10 is 270.

This is because, 260 will be short of want the manager want however ordering for 270 will be in excess with three seats.

Hence the manager will order 270 and heave 3 extra seats

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Domain: (-6, -1]

This is where the graph lines up with the x-axis.

Range: [-6, 4)

This is where the graph lines up with the y-axis.

See the two pictures for a visual reason why.

The minimal approximation error A-A 2achievable by a rank-1 approximation A to A is

||A - A1||₂=0 where A is 2×2 matrix.

We have given a matrix A as seen in above figure or A = [ 5 15 ; 6 18 ; -1 -3 ; -4 -12 ; 2 6]

note here that C₂= 3C₁

where Cᵢ --> iᵗʰ column

v = [ 5 ; 6 ; -1 ; -4 ; 2]

||v||² = 82 => ||v|| = √82

and A At v = 820 v

and A At = [ 82 246 ; 246 738]

AAt [1;3] = 820[1;3]

=> v1 = 1/√10(1,3)^t

Then the best rank of 1 approx

= √820 /√80√10 [ 5 ; 6 ; -1 ; -4 ; 2] [ 1 3]

= A

Since , the rank of matrix A is one so, the minimal approx. value is ||A - A1||2 = 0

Hence, the minimal Approx. ||A - A1||2 = 0 .

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Complete question:

Consider the matrix A: A = [5 15] 6 18 -1 -3 -4 -12 [26] What is the minimal approximation error A-A 2 achievable by a rank-1 approximation A to A? Hint: Can you determine this without explicitly calculating the SVD?