How many solutions does the system of equations have? y = −7/2 x + 11 7x + 2y = 20
1 solution no solution infinitely many solutions cannot be determined

Answer:

[tex]a_{n}[/tex] = 6n - 5

Step-by-step explanation:

there is a common difference between consecutive terms in the sequence, that is

7 - 1 = 13 - 7 = 19 - 13 = 6

this indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 1 and d = 6 , then

[tex]a_{n}[/tex] = 1 + 6(n - 1) = 1 + 6n - 6 = 6n - 5

If the numbers of subsets of {1, 2, 3, 4, 5, 6, 7, 8, 9} that are subsets of neither {1, 2, 3, 4, 5} nor {4, 5, 6, 7, 8, 9} is K, then the sum of digits of K is 9

Let the sets be

A =  {1, 2, 3, 4, 5, 6, 7, 8, 9}

B = {1, 2, 3, 4, 5}

C = {4, 5, 6, 7, 8, 9}

Then

B ∩ C = {4, 5}

Subsets of B ∩ C = {4}, {5}, {4,5}, {}

If we exclude the null set then the subsets remaining will be {4}, {5}, {4,5}

No. of elements in A = 9

No. of subsets of A = [tex]2^9[/tex]

No. of elements in B = 5

No. of subsets of B = [tex]2^5[/tex]

No. of elements in C = 6

No. of subsets of C = [tex]2^6[/tex]

If we subtract the no. of subsets of B and C from the no. of subsets of A we get the no. of subsets of A that are not the subsets of B or C

But the null set will be subtracted twice

Also as the subsets of B ∩ C excluding null set will be subtracted twice

Therefore, total number of subsets of A not the subsets of B or C

[tex]k=2^9-2^5-2^6+1\\k=512-32-64-2\\\\k=414[/tex]

The sum of the digits of k=9

The complete question is-

If the numbers of subsets of {1, 2, 3, 4, 5, 6, 7, 8, 9} that are subsets of neither {1, 2, 3, 4, 5} nor {4, 5, 6, 7, 8, 9} is K, then find the sum of digits of K.

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You can fill in the rest of the table as shown below.

The derivative of a function is a concept from calculus that measures the rate of change of a function at a specific point. It provides information about how the value of the function changes as its input changes.

Use the following differentiation rules to fill the table:

d/dx(f(x)·g(x)) = f(x)·g'(x) + f'(x)·g(x)         (product rule)

d/dx(f(x)/g(x)) = [ g(x)·f'(x) - f(x)·g'(x) ] / [(g(x))²]   (Quotient rule)

d/dx(g(x)/f(x)) = [ f(x)·g'(x) - g(x)·f'(x) ] / [(f(x))²]     (Quotient rule)

x    f(x)   f'(x)   g(x)  g'(x)    d/dx(f(x)·g(x))     d/dx(f(x)/g(x))    d/dx(g(x)/f(x))

0    3       -2    -4     3            17                      -1/16                    1/9

1     2       -1      1      0            -1                         -1                      1/4

2    4        2     3      1            10                       2/9                    -1/8

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Answer:

10x = 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5

Step-by-step explanation:

Distributive property of multiplication says every element within every pair of elements is added and multiplied to each other. So the value of 10 times that of 5 is 50.

The value of the network density is 0.9

Since the potential connections (PC) formula is n(n-1)/2 and number of nodes is 5 (i.e. n = 5). We have:

PC = n(n-1)/2

PC = 5(5-1)/2

PC = (5*4)/2

PC = 20/2

PC = 10

Actual connection (AC) = 9

Network Density = AC/PC

Network Density = 9/10

Network Density = 0.9

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The simplified expression is cos(x) of trigonometric expression  (sin (30° + x)+sin (30° - x))

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We can simplify this expression using the sum-to-product formula for sine:

sin(a + b) + sin(a - b) = 2 sin(a) cos(b)

Let's use this formula by setting a = 30° and b = x:

sin(30° + x) + sin(30° - x) = 2 sin(30°) cos(x)

We know that sin(30°) = 1/2, so we can substitute:

sin(30° + x) + sin(30° - x) = 2(1/2) cos(x)

sin(30° + x) + sin(30° - x) = cos(x)

Therefore, the simplified expression is cos(x).

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Answer:

380

Step-by-step explanation:

(34 * 10) + (4 x 10) =

= 10 * (34 + 4) =

= 10 * 38 =

= 380

The equation for v is ±√k/m

Two or more expressions with an Equal sign is called as Equation.

The given equation is k=mv²

k equal to m times of v square.

Where k is a formula of kinetic energy.

We need to solve for v

To do this we have to isolate the variable v

To isolate the variable v we have to Divide both sides by m

v²=k/m

v square equal to k by m.

Square root on both sides.

v=±√k/m

v equal to plus or minus square root of k by m.

Hence, the equation for v is ±√k/m

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Relationship among AC, A'C', and A"C'' is all the three sides are corresponding sides

a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".

To widen or enlarge an opening or hollow structure beyond its usual size in simple way changes the the size.

The scale factors is the factor in which each linear measure of the figure is multiplied.

AC is a smaller triangle which is dilated to get A'C' and this A'C' is dilated to get A''C''.

the relationship among AC, A'C', and A"C'' is all the three sides are corresponding sides with a scale factor.

Hence,  relationship among AC, A'C', and A"C'' is all the three sides are corresponding sides

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Answer:

N?A

Step-by-step explanation:

Answer:

325 is a hundred times bigger than 32500

Step-by-step explanation:

if it is ten times bigger, add one 0 at the end

if it is one hundred times bigger, add two 0 at the end

In the algebra on of the form of sequence is arithmetic progression or sequence which is described below.

In the arithmetic sequence  the common difference between any two consecutive terms remains constant .

In this sequence we can get the next term by adding one fixed value which is known as a common difference. It is also known as arithmetic progression(AP).

Formula for any nth term in AP,

T = a + nd

d = T₂-T₁

Where, a is first term , n is nth term and d is common difference

If aₙ = aₙ₋₁  -4

where aₙ is a nth term and aₙ₋₁ is a (n-1)th term

Now,

a + nd  = a + (n-1-1)d - 4

nd   = (n - 2)d - 4

nd = nd -2d - 4

2d = -4

d = -2

So, aₙ = a -2n

aₙ₋₁ = a -2(n - 2)

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Answer:

- It is a parallelogram

Step-by-step explanation:

- The interior angle sum of a quadrilateral is 360°

Considering the four angles;

[tex]{ \tt{m \angle A + m \angle B + m \angle C + m \angle D = 360 \degree}} \\ \\ { \tt{(x + 12) + \{2(x + 3) \} + ( \frac{3}{2} x - 15) + ( \frac{7}{3} x - 12) = 360}} \\ \\ { \tt{(x + 2x + \frac{3}{2}x + \frac{7}{3}x) + (12 + 6 - 15 - 12) = 360 }} \\ \\ { \tt{ \frac{41}{6} x - 9 = 360}} \\ \\ { \tt{ \frac{41}{6}x = 369 }} \\ \\ { \tt{41x = 2214}} \\ \\ { \tt{x = 54}}[/tex]

- Therefore, substitute in x and find the angles.

[tex] { \tt{m \angle A = (x + 12) = (54 + 12) = 66 \degree}} \\ \\ { \tt{m \angle B = 2(x + 3) = 2(54 + 3) = 114 \degree}} \\ \\ { \tt{m \angle C = ( \frac{3}{2}x - 15) = \{( \frac{3}{2} \times 54) - 15 \} = 66 \degree }} \\ \\ { \tt{m \angle D = ( \frac{7}{3}x - 12) = \{( \frac{7}{3} \times 54) - 12 \} = 114 \degree }}[/tex]

Answer:

58% decrease

Step-by-step explanation:

The slope of the line on the graph is equal to: A. -1/3.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Based on the information provided, we can logically deduce the following data points on the line:

Points on x-axis = (-2, 4).

Points on y-axis = (2, 0).

Substituting the given data points into the slope formula, we have the following;

Slope, m = (0 - 2)/(4 + 2)

Slope, m = -2/6

Slope, m = -1/3.

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Answer:

Step-by-step explanation:

The frequency of a cosine function is related to the number of cycles that the function completes in a unit interval (usually in 2π radians).

The frequency of a cosine function with the form f(x) = A * cos(Bx + C) is given by B/(2π), where A, B, and C are constants.

For the function f(x) = 9cos(4πx) + 10, the frequency is given by 4π / (2π) = 2 cycles per unit interval.

So, the frequency of the function f(x) = 9cos(4πx) + 10 is 2 cycles per unit interval.

The slope of the line in graph 2 is equal to 1.

The slope of the line in graph 3 is equal to 1/2.

The slope of the line in graph 4 is equal to 3/4.

The slope of the line in graph 5 is equal to 3.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substituting the given data points into the slope formula, we have the following;

Slope, m = (7 - 2)/(7 - 2)

Slope, m = 5/5

Slope, m = 1.

For the line in graph 3 with the given data points, we have:

Slope, m = (3 + 2)/(6 + 4)

Slope, m = 5/10

Slope, m = 1/2.

For the line in graph 4 with the given data points, we have:

Slope, m = (6 - 0)/(8 - 0)

Slope, m = 6/8

Slope, m = 3/4.

For the line in graph 5 with the given data points, we have:

Slope, m = (6 - 0)/(2 - 0)

Slope, m = 6/2

Slope, m = 3.

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Answer:

Step-by-step explanation:

To determine the character of the solutions of the equation in the complex number system, we need to analyze the nature of the coefficients of the equation, specifically the discriminant, which is obtained by the equation: b^2 - 4ac, where a, b and c are the coefficients of the equation.

In this case, the equation is

3x^2 + 7x - 3 = 0

So, the coefficients are a = 3, b = 7, and c = -3.

We can now calculate the discriminant as follows:

b^2 - 4ac = 7^2 - 4 * 3 * -3 = 49 + 36 = 85

Since the discriminant is positive, we know that the equation has two distinct real solutions. The exact solutions can be obtained using the quadratic formula, but that's not required to determine the character of the solutions.

Therefore, the equation has two real solutions.

The number of ways for the child to select 3 treats is given as follows:

455 ways.

The number of different combinations of x objects from a set of n elements is obtained with the formula presented as follows, using factorials.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The order in which the treats are chosen is not relevant, hence the combination formula is used to solve this question.

Three treats are chosen from a set of 15, hence the number of ways is given as follows:

C(15,3) = 15!/(3! x 12!) = 455 ways.

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Answer:

(-10, 12).

Step-by-step explanation:

A dilation with a scale factor of 2 centered at the origin expands distances from the origin by a factor of 2. If a point in the plane is represented by the coordinates (x, y), then the point obtained by a dilation centered at the origin with scale factor k is represented by (kx, ky).

So, if the original point is (-5, 6), then after the dilation of 2 centered at the origin, the new point is represented by (2 * -5, 2 * 6) = (-10, 12).

So the coordinates of (-5, 6) after a dilation of 2 centered at the origin are (-10, 12).

Answer:

The rate of change of the velocity of the wave with respect to the depth of the water is 3/2 meters per second per meter when the depth is 2 meters. This can be found by taking the derivative of v(h) with respect to h, which is 3/2√h. When h is 2, the rate of change is 3/2√2, which is equal to 3/2 meters per second per meter.

Answer:

Option A

Step-by-step explanation:

A = opposite/hypotenuse = 12/5

I don't really have anymore explanation I could give you because that just what I could think of!

Answer: I think D. Sin A…..

Step-by-step explanation: hope this helps:)

The type of number types that are being described are A. Rational, integer.

A rational number in mathematics is one that can be stated as the quotient or fraction of two integers, p and q, with p being the numerator and q being the denominator, respectively.

Therefore, whole numbers are the numbers 0, 1, 2, 3, 4 and so on and negative numbers are not considered whole numbers.

natural numbers are called the counting numbers that are the numbers 1, 2, 3, 4, and so on. they are positive numbers and zero is not considered a natural number as you can see.

integers are all the whole numbers and their opposite (negative) but negative numbers are NOT whole or natural numbers. fractions and decimals are not integers.

irrational numbers are an infinite number of digits to the right of the decimal point, without repeating.

Thus, option A is the answer

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Classify the real number. (Choose all that apply). –9 A.) Rational B.) Whole C.) Irrational D.) Natural E.) Integer

The completed proof that demonstrates that: ΔLMN ≅ ΔLON is:

The Angle-Angle-Side Postulate (AAS) is a rule used in geometry to prove that two triangles are congruent. It states that if two angles and the side between them in one triangle are congruent to two angles and the side between them in another triangle, then the two triangles are congruent.

The reflexive property of equality in algebra asserts that a number is always equal to itself. Equality has a reflexive attribute. If x positive integer, then x = x.

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Answer:

b

Step-by-step explanation:

make sure the y axis doesnt repeat

Answer:1/2 head and 1/2 tails

Step-by-step explanation: no.of experiments for heads = 5

total no of experiments=10

probability=5/10=1/2

no.of experiments for  = 5

total no of experiments=10

probability=5/10=1/2

The value of x for the angle C in the triangle ABC is equal to 42.5

A triangle formed by the diameter of a circle is a right triangle, with one side being the diameter of the circle and the other two sides being radii of the circle. Since the diameter of a circle bisects the circle into two equal halves, it also bisects the right angle formed by the radii into two equal angles of 45 degrees each.

The angle C is equal to 90° and we shall solve for the value of x as follows:

2x + 5 = 90°

2x = 90° - 5 {subtract 5 from both sides}

2x = 85°

x = 85°/2 {divide through by 2}

x = 42.5

Therefore, the value of x for the angle C in the triangle ABC is equal to 42.5

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Answer: no one cares

Step-by-step explanation:

Answer:

Step-by-step explanation:

The effective tax rate is the amount of tax paid as a percentage of the total purchase price. To calculate the effective tax rate, you can divide the amount of tax by the total purchase price and multiply the result by 100 to get the answer as a percentage.

In this case, the effective tax rate would be:

(1200 / 24000) * 100 = 5%

So Chris's effective tax rate on the purchase of his car is 5%.

The boat's displacement is approximately 84,016.8 metric tons.

To convert the boat's top speed from knots to miles per hour, we can use the conversion factor of 1.15078 miles per hour per knot:

26 knots × 1.15078 miles per hour per knot = 29.86 miles per hour (rounded to two decimal places)

Therefore, the boat's top speed is approximately 29.86 miles per hour.

To convert the boat's displacement from tons to metric tons, we can use the conversion factor of 0.907185 metric tons per ton:

93,000 tons × 0.907185 metric tons per ton = 84,016.8 metric tons (rounded to one decimal place)

Therefore, the boat's displacement is approximately 84,016.8 metric tons.

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