In triangle nql, point s is the centroid, ns = (x + 10) feet, and sr = (x + 3) feet. Triangle n q l has centroid s. Lines are drawn from each point to the midpoint of the opposite side to form line segments n r, q m, and l p. The length of line segment n s is x + 10 and the length of line segment s r is x + 3. What is rs?.

Answer:

3/4

Step-by-step explanation:

Gradient=6/8=3/4

For the inductive step, assuming the statement holds for a graph with n components, where n < k, we consider a graph with (n + 1) components. By removing one vertex from one of the components, we create a new graph with k - 1 vertices and n components. By the induction hypothesis, this new graph has at least (k - 1) - n edges. Adding back the removed vertex and connecting it to the n components creates at least one new edge in each component. Therefore, the total number of edges in the original graph is at least k - 1.

Thus, by induction, it is proven that if a simple graph has n components, it has at least k - n edges.

To prove the statement by induction, we need to establish a base case and an inductive step.

**Base case:**

When the graph has only one component (n = 1), it means that all k vertices are connected, forming a single connected component. In this case, the number of edges in the graph is maximized, and it can be calculated using the formula for a complete graph with k vertices.

The number of edges in a complete graph with k vertices is given by the formula: E = k(k-1)/2.

Since there is only one component, and it is a complete graph, the number of edges in the graph is E = k(k-1)/2.

Now, let's substitute n = 1 in the statement we need to prove:

"If a simple graph has n components (n = 1), then it has at least k - n edges."

Plugging in the values:

"If a simple graph has 1 component, then it has at least k - 1 edges."

From the base case, we can see that the graph indeed has k - 1 edges when it has only one component.

**Inductive step:**

Assume the statement holds for a graph with n components, where n < k. We will prove that it holds for a graph with (n + 1) components.

Let G be a simple graph with k vertices and (n + 1) components. We can remove one vertex from one of the components to create a new graph G'. The new graph G' will have k - 1 vertices and n components.

By the induction hypothesis, G' has at least (k - 1) - n edges.

Now, let's consider the original graph G. When we add back the vertex we removed, it can be connected to any of the n components in G'. This addition of the vertex creates at least one new edge in each of the n components.

Therefore, the total number of edges in G is at least the number of edges in G' plus the number of new edges added by the vertex. Mathematically, it can be expressed as:

Edges(G) ≥ Edges(G') + n

Since Edges(G') + n = ((k - 1) - n) + n = k - 1, we have:

Edges(G) ≥ k - 1

Hence, we have proved that if a simple graph has n components, it has at least k - n edges.

By the principle of mathematical induction, the statement is true for all values of n such that 1 ≤ n < k.

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Answer:

79

Step-by-step explanation:

80 divided by 8+72-3

10+72-3

82-3

79

Hope this helps!

The number we are looking for is x - 6.

To determine the number that, when subtracted from x, results in 6, we can set up the equation:

x - y = 6

Here, y represents the unknown number we are trying to find. To isolate y, we can rearrange the equation:

y = x - 6

Therefore, the number we are looking for is x - 6.

It's important to note that in mathematics, without specific values or additional information about x, we cannot determine a unique solution. The expression "6 - xx - 66 + x6 - ( x - 6)" you provided is not clear and does not allow us to solve for x or the unknown number directly. If you have specific values or additional context, please provide them, and I'll be glad to assist you further.

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Answer:

heyy do you still need help

Step-by-step explanation:

Answer:

105

Step-by-step explanation:

The total angle in a parallelogram is 360

Answer:

i. Area(A)=L×B

24.5m×18

441m²

Answer:

So The Answer would be 600=1.05x and 600=1.06x for part A and B

Step-by-step explanation:

For Part B If there goal is to raise 600$ then 5% of 600$ = 30$ per roll of wrapping paper;

Part A: 600= 1.05x

The expression 1.05 represents the 5% increase for X wrapping paper sold to the equivalent of 600$  

For end of the Question Im unsure what they mean they "missed there goal of raising 5600?.. 5600$ or 560.0$?"

The value(s) of k such that the limit of f(x) exists as x approaches 1 are k = ±√15.

To find the value(s) of k, we need to ensure that the left-hand limit and the right-hand limit of f(x) as x approaches 1 are equal.

For x < 1, the expression for f(x) is 7x² - k²x. To find the left-hand limit, we substitute x = 1 into this expression:

lim(x→1-) f(x) = 7(1)² - k²(1) = 7 - k²

For x > 1, the expression for f(x) is 15 + 8kx² + k cos(1 - x). To find the right-hand limit, we substitute x = 1 into this expression:

lim(x→1+) f(x) = 15 + 8k(1)² + k cos(1 - 1) = 15 + 8k + k cos(0) = 15 + 8k + k

To ensure that the limit exists, the left-hand limit and the right-hand limit must be equal:

7 - k² = 15 + 8k + k

Rearranging the equation:

k² + 7k - 8 = 0

Factoring:

(k - 1)(k + 8) = 0

From this, we find two possible values for k: k = 1 and k = -8.

The value(s) of k such that the limit of f(x) exists as x approaches 1 are k = ±√15. These values ensure that the left-hand limit and the right-hand limit of f(x) are equal, satisfying the condition for the existence of the limit.

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Answer:

A. F'G' = 3 & G'H' = 5.

Step-by-step explanation:

Translations of any shape will not change the side lengths and will be congruent to the original shape.

\(10 ^{2y} = 25\)

\( {10}^{y} = .......\)

\(10 ^{2y} = 25\)

\( (10y {)}^{2} = {5}^{2} \)

\(10y = 5\)

\( \frac{1}{ {10}^{y} } = \frac{1}{5} \)

\( {10}^{ - y} = \frac{1}{5} \)

therefore, the correct answer is option E.

the correct option is option e.

hope this helps you

have a great day

please give me brainliest.

The value of the coefficients a, b, c, and constant d will be 0.50, 0, -1.50, and 1, respectively.

Let a, b, c, and d are the zeroes of the polynomial and k be the leading corefficient. Then the polynomial is given as,

⇒ k(x - a)(x - b)(x - c)(x - d)

The degree of the polynomial will be greater than or equal to the number of zeroes.

From the graph, the zeroes are -2, 1, and 1. Then the polynomial is given as,

y = a(x + 2)(x − 1)²

The curve passes through (0, 1), then we have

1 = a(0 + 2)(0 − 1)²

1 = 2a

a = 1/2

a = 0.5

Then the polynomial is given as,

y = 0.50 (x + 2)(x − 1)²

y = 0.50 (x + 2)(x² + 1 - 2x)

y = 0.50 (x³ + 2x² + x + 2 - 2x² - 4x)

y = 0.50 (x³ - 3x + 2)

y = 0.50x³ - 1.5x + 1

Compare with standard equation, then we have

a = 0.50

b = 0

c = - 1.5

d = 1

The value of the coefficients a, b, c, and constant d will be 0.50, 0, -1.50, and 1, respectively.

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The missing graph is attached below.

The ratio of apples to oranges, written as a fraction If Keenan makes a basket with 6 apples, is 5 / 4.

Only verbal descriptions of a portion of the whole were used to write fractions in ancient Rome. The numerator and denominator of fractions are first written in India with one number above the other but without a line. The line used to divide the numerator and the denominator were only added by Arabs.

Given:

For every 4 oranges, there are 5 apples,

Keenan makes a basket with 6 apples,

Calculate the number of oranges as shown below,

The number of oranges = 4 / 5 × 6 = 24 / 5

Calculate the fraction of apples to oranges as shown below,

Ratio = The total number of apples / The number of oranges

Ratio = 6 / 24 / 5

Ratio = 30 / 24

Ratio = 5 / 4

Thus, the ratio is 5 / 4.

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The complete question is:

For every 4 oranges, there are 5 apples, If Keenan makes a basket with 6 apples, what is the ratio of apples to oranges written as a fraction?

Answer:

D

Step-by-step explanation:

Answer:

the answer is: parallelograms are quadilaterals

Answer:

x ≈ 33.4

Step-by-step explanation:

Using the sine ratio in the right triangle

sin46° = \(\frac{opposite}{hypotenuse}\) = \(\frac{24}{x}\) ( multiply both sides by x )

x × sin46° = 24 ( divide both sides by sin46° )

x = \(\frac{24}{sin46}\) ≈ 33.4 ( to the nearest tenth )

Answer:

1

Step-by-step explanation:

When you find the absolute value of -2, it is 2, since that is how far away from the point 0 on a line. When you divide 2 by 2, it equals 1.

Answer: h(-2) = 1

Step-by-step explanation:

1. Substitute the -2 in for x

h(-2) = l(-2)l / 2

2. Apply the absolute value signs to the -2 making it positive:

h(-2) = 2/2

3. Solve:

h(-2) = 1

Hope this helps :)

Therefore, the sample of 5 books selected for inspection is: 37569, 85187, 44692, 50706, and 53161.

by the question.

To select a simple random sample of 5 books from the population of 7070 textbooks, Mr. Thompson can use the following procedure:

Assign a unique number to each book in the population, from 0101 to 7070.

Generate a sequence of five random digits from 0 to 9 using the random digit table provided.

Use each digit as an index to select one book from the population, starting from the first book listed in the table.

Here is the step-by-step process to select the sample:

Assign numbers to the books from 0101 to 7070.

Generate a sequence of five random digits from the random digit table:

37569

Use each digit as an index to select one book from the population:

Book 3 corresponds to the first digit, 3.

Book 7 corresponds to the second digit, 7.

Book 5 corresponds to the third digit, 5.

Book 6 corresponds to the fourth digit, 6.

Book 9 corresponds to the fifth digit, 9.

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Answer:

Step-by-step explanation:

State promise

The two rocks share the option C. State.

Physical properties are properties of a substance which does not involve any chemical composition or changes in the substance.

Examples are color, density, hardness, and so on.

Given are two rocks.

Clearly, from the picture, we can say that shininess is different. The first rock is more shining.

Clearly colors are also not same.

Regarding the state of both rocks, both rocks are solid. So they share the property of state.

Texture is also different for both. Second one is harder texture.

Hence the physical property that both rocks share is state.

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The Figure A and Figure B show starting steps in the construction of an equilateral triangle.

According to the statement

we have to find the correct figure which show the starting steps in the construction of an equilateral triangle.

So, For this purpose, we know that the

Construction of equilateral triangle inscribed in the circle is :

Place your compass point on the paper and draw a circle. (Keep this compass span!)

2. Place a dot, labeled A, anywhere on the circumference of the circle to act as a starting point.

3. Without changing the span on the compass, place the compass point on A and swing a small arc crossing the circumference of the circle.

4. Without changing the span on the compass, move the compass point to the intersection of the previous arc and the circumference and make another small arc on the circumference of the circle.

5. Keep repeating this process of "stepping" around the circle until you return to point A.

6. Starting at A, connect every other arc on the circle to form the equilateral triangle.

By this way we construct a triangle.

And from the given figures

The figure A and B shows the perfect construction because it follows all the construction steps.

So, The Figure A and Figure B show starting steps in the construction of an equilateral triangle.

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Disclaimer: This question was incomplete. Please find the full content below.

Question:

Select all the correct figures. Which figures show starting steps in the construction of an equilateral triangle

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Answer:

Step-by-step explanation:

5x +2.57=25.92

5x=23.35

23.35/5

x=4.67

To solve for the IS-LM equilibrium in an economy, we need to calculate the IS equation, LM equation, equilibrium level of income, and equilibrium level of interest rate. Given the functions for consumption (C), saving (S), investment (I), money supply (Ms), and money demand (Md), we can derive these values.

(a) IS equation:

The IS equation represents the equilibrium condition in the goods market. It is derived by equating national income (Y) with aggregate demand (C + I + G), where G represents government spending. In this case, the equation is:

Y = C + I

Substituting the given consumption and investment functions, we have:

Y = (100 + 0.8Y) + (120 - 5r)

Simplifying the equation, we get:

Y = 220 + 0.8Y - 5r

(b) LM equation:

The LM equation represents the equilibrium condition in the money market. It is derived by equating money supply (Ms) with money demand (Md). In this case, the equation is:

Ms = Md

Substituting the given money supply and money demand functions, we have:

120 = 0.2Y - 5r

(c) Equilibrium level of income:

To find the equilibrium level of income, we solve the IS equation for Y. Rearranging the IS equation from part (a), we get:

0.2Y = 220 - 5r

Y = (220 - 5r) / 0.2

(d) Equilibrium level of interest rate:

To find the equilibrium level of interest rate, we solve the LM equation for r. Rearranging the LM equation from part (b), we get:

5r = 0.2Y - 120

r = (0.2Y - 120) / 5

By substituting the equilibrium level of income (Y) into the LM equation, we can find the corresponding equilibrium level of interest rate (r). Similarly, by substituting the equilibrium level of interest rate (r) into the IS equation, we can find the corresponding equilibrium level of income (Y). These values represent the IS-LM equilibrium in the economy.

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Answer:

12, 30, 36, 48

Step-by-step explanation:

Answer:

2?

Step-by-step explanation:

I couldn't find an answer but 2 was the most appropriate so try that, and sorry I wasn't much of a help

Answer:

2

Step-by-step explanation:

4/14 does not = 6/20

2/12 does not = 3/18

Thus, NEITHER is the answer.

Answer:

80 cookies per hour

Step-by-step explanation:

First, let's make 3 1/2 a decimal, so that would be 3.5. Now lets make this problem a proportion. 280/3.5 means that Stan makes 280 cookies every 3.5 hours.

Let's simply this proportion to find the unit rate. 3.5 divided by 3.5 is 1, so dividing by 3.5 will help find the unit rate. We already did the bottom, so let's do the top. 280 divided by 3.5 is 80.

Therefore the unit rate is 80.

Hope I helped!!!

The values of a and b that make the piecewise defined function f(x) = 3x + 4, for x < -3, and f(x) = 2x^2 + ax + b, for x > -3, both continuous and differentiable everywhere are a = 6 and b = 9.

To ensure that the piecewise defined function is continuous at the point where x = -3, we need the left-hand limit and right-hand limit to be equal. The left-hand limit is given by the expression 3x + 4 as x approaches -3, which evaluates to 3(-3) + 4 = -5.

On the right-hand side of the function, when x > -3, we have the expression 2x^2 + ax + b. To find the value of a, we need the derivative of this expression to be continuous at x = -3. Taking the derivative, we get 4x + a. Evaluating it at x = -3, we have 4(-3) + a = -12 + a. To make this expression continuous, a must be equal to 6.

Next, we find the value of b by considering the right-hand limit of the piecewise function as x approaches -3. Substituting x = -3 into the expression 2x^2 + ax + b, we get 2(-3)^2 + 6(-3) + b = 18 - 18 + b = b. To make the function continuous, b must equal 9.

Therefore, the values of a and b that make the piecewise defined function both continuous and differentiable everywhere are a = 6 and b = 9.

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Answer:

8551.56

Step-by-step explanation:

\(A=5300(1+(0.08)/12)^{(12)(6)} \approx 8551.56\)

Answer:

6 units

Step-by-step explanation:

Let's call the length of the rectangle "L" and the width "W".

From the problem, we know that the width is 2 units less than the length, so we can write:

W = L - 2

We also know that the area of the rectangle is 48 square units, so we can write:

A = L * W

Substituting the first equation into the second equation, we get:

48 = L * (L - 2)

Expanding the brackets, we get:

48 = L^2 - 2L

Rearranging, we get:

L^2 - 2L - 48 = 0

Now we can use the quadratic formula to solve for L:

L = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 1, b = -2, and c = -48. Substituting these values into the formula, we get:

L = (2 ± sqrt(4 + 192)) / 2

L = (2 ± sqrt(196)) / 2

L = (2 ± 14) / 2

So, L = 8 or L = -6. We can ignore the negative solution, so the length of the rectangle is 8 units.

Now we can use the first equation to find the width:

W = L - 2

W = 8 - 2

W = 6

Therefore, the width of the rectangle is 6 units.