please help with this by showing work
8. Find the equation for the line that passes through the points: (-2,5) and (7,3). Give your answer in point-slope form.

Answer:

x^2 = 9x

x^2 - 9x = 0

x(x-9) = 0

x=0 or x=9

Step-by-step explanation:

The number is 9.

Translate the statement into an equation, then solve for the unknown number.

Let the unknown number be represented as x.

Thus:

square of the number can be translated as [tex]x^{2}[/tex]

[tex]9 \times $ the $ number = 9x[/tex]

Therefore:

[tex]x^{2} = 9x[/tex]

Solve for x

[tex]x^{2} - 9x = 0[/tex]

Factorize

[tex]x(x - 9) = 0\\x = 0 $ or \\x - 9 = 0\\x = 9[/tex]

The unknown number cannot be 0, therefore, the number is 9.

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TRUE A natural number is another name for the counting number.

Natural numbers are those in mathematics that are utilized for counting and ordering.

Cardinal numbers are those used for counting, and ordinal numbers are those used for ordering.

The term "counting numbers" refers to all natural numbers. These are always positive whole numbers, such as 1, 2, 3, 4, 5, and 6.

Mathematical number systems depend heavily on the infinite counting numbers, which can be counted.

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 The total debt of the government at the end of year three is $7.2 billion.

Starting with a total debt of $5.5 billion, the government's deficits of $600 million in year one and $1.5 billion in year two contribute to an increase in the debt. However, in year three, the government runs a surplus of $400 million, which helps reduce the debt.

Thus, the total debt at the end of year three is calculated by adding the initial debt and deficits, and subtracting the surplus. In this case, the total debt at the end of year three is $7.2 billion.

Assuming the government runs a deficit of $200 million in year three, the calculation changes. With the initial debt of $5.5 billion, the deficits of $600 million in year one and $1.5 billion in year two, and the additional deficit of $200 million in year three, the total debt at the end of year three would be $7.8 billion. This demonstrates how the deficit amounts impact the overall debt accumulation.

If a government runs a budget deficit of $5 billion each year for ten years, resulting in a total deficit of $50 billion, followed by a surplus of $2 billion per year for five years, reducing the debt by $10 billion, and then maintaining a balanced budget for another ten years, the government debt would amount to $40 billion. The deficits over the initial ten years lead to a significant accumulation of debt, but the subsequent surpluses help mitigate the debt by reducing the deficit. Finally, the balanced budget in the later years ensures that there is no further increase in debt. Understanding the interplay between deficits, surpluses, and a balanced budget is crucial to grasp the long-term implications on government debt and fiscal stability.

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The final answer rounded to 5 decimal places is:`x = 0.57735`

A) Given trigonometric expression is;`sin (π/6) + cos (π/6)`

Using the trigonometric values of π/6 from the trigonometric table, we have:

sin π/6 = 1/2cos π/6 = √3/2.Substituting the trigonometric values into the given expression, we have:

sin π/6 + cos π/6= 1/2 + √3/2= (1 + √3)/2

Therefore, the value of `sin (π/6) + cos (π/6)` is `(1 + √3)/2`.

B) Now, coming to the next part, we need to find the side labeled x.

The value of the tangent of an angle is equal to the ratio of the opposite side and the adjacent side. Thus, we can write:tan θ = Opposite side/Adjacent side

We have the values of the angle and the adjacent side, using that, we can find the opposite side as follows:`

tan 30° = Opposite side/1`Opposite side = `tan 30°`Opposite side = `(1/√3)`

Therefore, the side labeled x is `(1/√3)`.

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Answer:

Step-by-step explanation:

the way it is written, the answer is

5x^2 - 6x + 2 + 19x - 7

5x^2 + 13x - 5    is the answer.

However I suspect you mean

5x^2 - 6x + 2 + 9x^2 + 10x - 7

14x^2 + 3x - 5    is the answer if the revision I've made is correct.

Answer:

C. 3a + 6

Step-by-step explanation:

The expression that describes the verbal expression is 3a + 6.

Now let us approach this step wisely;

  Triple quantity a = 3a

Increased by 6 =  + 6 , an increment is addition to a term.

So, the full algebraic expression is 3a + 6

The solution is 3a + 6. Word problems like this should be approached step wisely.

Answer:

-5

Step-by-step explanation:

the answer, please give brainliest if u can

Answer:

a is 10

Step-by-step explanation:

parallel lines have the same slope, but a different y intercept

you would substitute the ordered pair in for x and y

y=-2x+10

Hope this helps :-)

Answer:tbh, that's impossible

Step-by-step explanation:

Given :

Natalie is going mountain biking. She can buy a bike for $250 or she can rent a bike for $30 an hour.

In both cases, she must also rent a helmet for $5 an hour.

To Find :

Which inequality shows the number of hours Natalie must bike for the cost of buying a bike to be less than renting a bike.

Solution :

Let, after t hours total money required is ( if she rent bike ).

T = 30t.

Money required to purchase bike , M = $250.

For cost of buying a bike to be less than renting a bike :

[tex]30t>250\\\\t > \dfrac{25}{3}\ hours\\\\t>8\dfrac{1}{3}\ hours\\\\t>8\ hours \ 20 \ minutes[/tex]

Hence, this is the required solution.

The properties of the function are

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

y = x² - 5

The vertex of the above function is

(0, -5)

The axis of symmetry is the x-coordinate of the vertex

So, we have

x = 0

The y-intercept is when x = 0

So, we have

y = -5

Because the leading coefficient is positive, the function has a minimum vertex

From the graph, we have the x-intercepts to be

x = ±2.236

The domain is the set of all real values, and the range is (-5, ∞)

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Answer:

73.5m

Step-by-step explanation:

4m fence casted a 7m high shadow 7/4 = 1.75, 42 x 1.75 = 73.5

Answer:

(-2, 1)

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

answer is just is 11

Step-by-step explanation:

let the two angles be x and x

since the sum of complementary angles is equal to 90 degree therefore according to question sum of x and x is equal to 90 degree

so the equation is

x + x =90

2x = 90

x= 90 /2

x= 45

There are 4 fast-food businesses in this small city that have only a drive-up window.

To determine the number of fast-food businesses that have only a drive-up window, we need to subtract the businesses that have a drive-up window and other services from the total number of businesses with a drive-up window.

According to the given information:

Total number of fast-food businesses = 22

Number of businesses with delivery service (D) = 7

Number of businesses with outside seating (O) = 13

Number of businesses with a drive-up window (W) = 13

Number of businesses with both a drive-up window and outside seating (W ∩ O) = 9

Number of businesses with both outside seating and delivery service (O ∩ D) = 3

Number of businesses with both delivery service and a drive-up window (D ∩ W) = 3

Number of businesses with all three services (D ∩ O ∩ W) = 2

To find the number of businesses with only a drive-up window:

Number of businesses with only a drive-up window = Number of businesses with a drive-up window (W) - Number of businesses with both outside seating and a drive-up window (W ∩ O)

Number of businesses with only a drive-up window = 13 - 9 = 4

Therefore, there are 4 fast-food businesses in this small city that have only a drive-up window.

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Answer:

D

Step-by-step explanation:

Equilateral triangle

An equilateral triangle will always have a perpendicular bisector that is also an angle bisector.

Option D is the correct answer.

We have,

In an equilateral triangle,

All sides are congruent, and all angles are congruent (each measuring 60 degrees).

The perpendicular bisector of any side of an equilateral triangle will also be an angle bisector, since it will pass through the vertex opposite to that side, dividing the angle into two congruent angles.

Thus,

An equilateral triangle will always have a perpendicular bisector that is also an angle bisector.

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answer:

4 is correct!

explanation:

hope this helped! <3 i answered your question & hope you have a great day! if you wouldn't mind could you pls give me brainliest? (im trying to level up) thanks! :)

Answer:

16$?

Step-by-step explanation:

8*2 = 16

If not pls specify question

Answer:

15-5y=20

15-20=5y

-5=5y

y=-1

Answer:

1

Step-by-step explanation:

[tex]swap \: - 5y \: and \: 15[/tex]

working step:

[tex]

15+−5y=20 \\

−5y+15=20 \\

−5y+15−15=20−15 \\

−5y=5 \\

−5y−5=5−5 \\

y=−1

[/tex]

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To calculate the cost of shortage (Cs), we need to find the area under the normal distribution curve to the left of the optimal service level. The cost of shortage is the difference between the selling price and the Monday price, multiplied by the probability of shortage.

To calculate the cost of excess (Ce), we find the area under the normal distribution curve to the right of the optimal service level. The cost of excess is the difference between the cost of making the cake and the selling price, multiplied by the probability of excess. The optimal service level is determined by minimizing the total cost, which is the sum of the cost of shortage and the cost of excess. We can find the corresponding z value for the optimal service level using the standard normal distribution table. Once we have the optimal service level (z value), we can find the corresponding demand value. Since demand is normally distributed, we can calculate the optimal number of birthday cakes to make for the weekend by subtracting the expected demand from the optimal service level demand. However, without specific information on the desired service level or target level of shortage/excess, it is not possible to provide numerical answers to the questions. The optimal service level, corresponding z value, and the optimal number of cakes will depend on the specific parameters and objectives of the supermarket bakery.

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Answer:

nobody cares

Step-by-step explanation:

a) The inflation rate at t = 1 is 0 and the output gap at t = 1 is 0.1.

b) So, 7₁ > 0 and To > 0 (As given, all parameters are > 0)

c) It is possible to stabilize inflation after only one period at B/p = (r - 7₁)/0.1

d) a higher ratio of on/oy is beneficial for inflation stabilization.

(a) Given,

Inflation target (π) = 0

Nominal interest rate (i) = F + t + t

Natural real interest rate (r) = 7 > 0

Output gap (y) = ỹt

Aggregate demand equation is t = -(rt-1- F) + πt-1 + ε

Aggregate supply equation is ỹt = ỹt-1+0t + e

Inflation rate (πt) = 0 for all t.

Nominal interest rate i = r + πt + ỹt

By Fisher identity, rt = it - πt

Now, for t = 0

Before the shock, i = r, π = 0 and y = 0

Given,

shock = 0.1

So, for t = 0,

output gap is given by

ỹt = ỹt-1+0t + e

= 0 + 0.1 + 0

= 0.1

Now, i = r + πt + ỹt

= r + 0 + 0.1

= r + 0.1

So, at t = 0, inflation rate π = 0 and output gap ỹ0 = 0.1

At t = 1

Inflation rate π1 = 0 (As given in the question)

Nominal interest rate i1 = r + π1 + ỹ1

So, we need to find ỹ1.

Now, putting the value of inflation rate and nominal interest rate in the Fisher identity, we get

rt-1 = i1 - π0

= r + ỹ1

Therefore, from the aggregate supply equation we ge

tỹ1 = ỹ0+0(ỹ1) +

e= 0.1 + e

Putting the value of ỹ1 in the nominal interest rate equation we get

i1 = r + π1 + ỹ1

= r + 0 + 0.1 + e

= r + 0.1 + e

(b) Given,o, B, p,

y < 1

Let ỹ0 = α

Then ỹ1 = 0.1 + e ≤ 1 (As given)

So, 0 ≤ ỹ1 ≤ 1

Now, from the aggregate supply equation we have,

ỹt = ỹt-1+0(ỹt) + e

As it is an increasing function of e and 0 < ỹ1 ≤ 1, we get ỹ2 < ỹ1 and 0 ≤ ỹ2 ≤ 1

So, 0 ≤ ỹt ≤ 1 for all t.

Hence, yo ≥ 0

Now, ỹ1 = α + 0.1 + e ≤ 1

So, α ≤ 0.9

So, 0 ≤ α ≤ 0.9

Now, let's calculate 7₁ and

π1.7₁ = rt-1

= i1 - π0

= r + ỹ1 - 0

= r + 0.1

So, 7₁ > 0 and To > 0 (As given, all parameters are > 0)

(c) Given, > 1

At time t = 0, the output gap is given by ỹ0 = α

Then, ỹ1 = 0.1 + e, and ỹ2 = 0.1 + 0 = 0.1

As ỹ2 is constant, it is clear that inflation will be stabilized after only one period.

To check this explicitly, let's calculate π1

Now, 7₁ = r + 0.1So, i1 = 7₁ + π1

By Fisher identity, i0 - π0 = rt-1

= r

Therefore, i0 = r + π0

So, the shock is given bye = ỹ1 - ỹ0-0(7₁)

= 0.1 - α

From the aggregate demand equation, we get

t = -(rt-1- F) + πt-1 + ε

= -(r - F) + 0 + ε

= -r + F + ε

Now, we can calculate inflation at t = 1 as

π1 = π0 + (1-B)(α - ỹ0) + B(π0 + o + y ỹ1) - p(7₁ - r)

π1 = 0 + (1-B)(α - α) + B(0 + o + y 0.1) - p(7₁ - r)

π1 = 0.1B - p(7₁ - r)

We want π1 = 0

So, 0.1B - p(7₁ - r) = 0

Thus, B/p = (r - 7₁)/0.1

Let B/p = ζ, then ζ = (r - 7₁)/0.1

Thus, it is possible to stabilize inflation after only one period at B/p = (r - 7₁)/0.1

(d) As we saw in part (c), a higher value of the ratio B/p results in the stabilization of inflation after only one period. Therefore, a higher ratio of on/oy is beneficial for inflation stabilization.

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Answer:

what

Step-by-step explanation:

To determine the percentage of Sara's students who answered at least half of the quiz questions incorrectly, we need more information than the relative cumulative frequency of students who earned a score of 21 or higher.

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Answer:

x>−4

Step-by-step explanation:

i hope this helps you

Answer:

b

Step-by-step explanation:

Answer:

A is the correct answer