What equation is graphed in this figure?

y-4= = -⅓(x+2)
y-3= ⅓(x + 1)
y+ 2 = -3(x - 1)
y - 5 = 3 (x - 1)​

(a) \(a+b-c\\-2+-3-4\\-5-4\\-9\)

(b) \(b+c^3\\-3+4^3\\-3+64\\61\)

(c)\(\frac{3b^2-c^2+a^2}{-3abc} \\\frac{3(-3)^2-(4)^2+(-2)^2}{-3(-2)(-3)(4)} \\\frac{3(9)-16+4}{6(-3)(4)} \\\frac{27-16+4}{-18(4)} \\\frac{11+4}{-72} \\\frac{15}{-72} \\-\frac{5}{24}\)

Answer:

The answer to (A) is -9.

The answer to (B) is 61.

The answer to (C) is \(-\frac{5}{24}\) in fraction form or -0.208 in decimal form.

Step-by-step explanation:

For problem (A), which is \(a+b-c\), in order to solve for this problem, plug in the information given from the question. The problem will look like \((-2)+(-3)-(4)\). Solve the problem by first adding (-2) + (-3), which equals (-5), and then, solve for (-5) -(4), which equals -9. The final answer for problem (A) will be -9.

For problem (B), which is \(b+c^{3}\), start by plugging in the information given from the question. The problem will look like \((-3)+(4)^{3}\). Solve the problem by cubing 4, which equals 64, and then, solve for (-3)+(64), which equals 61. The final answer for problem (B) will be 61.

For problem (C), which is \(\frac{3b^{2}-c^{2}+a^{2} }{-3abc}\),  start by plugging in the information given from the question. The problem will look like \(\frac{3(-3)^{2}-(4)^{2}+(-2)^{2} }{-3(-2)(-3)(4)}\). Solve the problem by first simplifying the numerator.

To simplify the numerator, raise -3 to the power of 2, which will equal 9, and multiplying 3 by 9, which will look like \(\frac{27-(4)^{2}+(-2)^{2} }{-3(-2)(-3)(4)}\). Next, raise 4 to the power of 2, which equals 16, and multiply -1 by 16, which will look like \(\frac{27-16+(-2)^{2} }{-3(-2)(-3)(4)}\). The next step is to raise -2 to the power of 2, which will look like \(\frac{27-16+4 }{-3(-2)(-3)(4)}\). Then, subtract 16 from 27, which equals 11, and add (11) + (4), which equals 15. The numerator equals 15.

Next, simplify the denominator. First, multiply -3 by -2, which equals 6, and the problem will look like \(\frac{27-16+4 }{6(-3)(4)}\). Then, multiply 6 by -3, which equals -18, and the problem will look like \(\frac{27-16+4 }{-18(4)}\). The next step is to multiply -18 by 4, which equals -72, and the denominator will equal -72.

Then, reduce the expression by cancelling the common factor, and the common factor is 3. The final answer will be \(-\frac{5}{24}\) in fraction form or -0.208 in decimal form.

Answer:

30 + 4 + .7 + .05

Step-by-step explanation:

You have to write them like that just like if you were to do 245 in expanded form it would be 200 + 40 + 5! Hope this helps!

Answer:

C. I and II

Step-by-step explanation:

In q1, all trig functions are positive. q2, sin and csc is positve. hope this helps!!

1. In the context of spacetime, the locus of points equidistant from the origin of a spacetime plane is a hyperbola.

In Euclidean space, the distance between two points is given by the Pythagorean theorem, which only considers spatial dimensions. However, in spacetime, the concept of distance is extended to include both spatial and temporal components. The spacetime distance, also known as the interval, is given by the Minkowski metric:

ds^2 = -c^2*dt^2 + dx^2 + dy^2 + dz^2,

where c is the speed of light, dt represents the temporal component, and dx, dy, dz represent the spatial components.

To determine the locus of points equidistant from the origin, we need to find the set of points where the spacetime interval from the origin is constant. Setting ds^2 equal to a constant value, say k^2, we have:

-c^2*dt^2 + dx^2 + dy^2 + dz^2 = k^2.

If we focus on a spacetime plane where dy = dz = 0, the equation simplifies to:

-c^2*dt^2 + dx^2 = k^2.

This equation represents a hyperbola in the spacetime plane. It differs from a circle in Euclidean space due to the presence of the negative sign in front of the temporal component, which introduces a difference in the geometry.

Therefore, the locus of points equidistant from the origin in a spacetime plane is a hyperbola.

(Note: The explanation provided assumes a flat spacetime geometry described by the Minkowski metric. In the case of a curved spacetime, such as that described by general relativity, the shape of the locus of equidistant points would be more complex and depend on the specific curvature of spacetime.)

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Answer:

25

Step-by-step explanation:

as you can see test a is further away from the ruler you have to put it at 0 so that you can get your answer I am not sure if it's correct or not

Answer:

Step-by-step explanation:

The value of the expression is approximately 1.132. First, we need to convert the angles from degrees to radians because trigonometric functions in calculators typically use radians as input.

To convert degrees to radians, we use the formula: radians = degrees x (π / 180)

So, we have:

 = 38.2° = 0.666 radians (approx.)

B = 146.4° = 2.552 radians (approx.)

Next, we can plug these values into the expression:

2cos(Â) + cos^2(B)

Substituting  and B with their respective values, we get:

2cos(0.666) + cos^2(2.552)

Using a calculator, we can evaluate this expression as follows:

2cos(0.666) + cos^2(2.552) ≈ 1.132

Therefore, the value of the expression is approximately 1.132.

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Answer:

m∠1=46°

m∠2=44°

m∠3=44°

m∠4=90°

m∠5=73°

m∠6=17°

m∠7=17°

The probability of adding either ground beef or onion as the first ingredient  0.25 or 25%.

If there are a total of 8 ingredients and 2 of them are either ground beef or onion, then the probability would be:

Probability = (Number of desired outcomes) / (Total number of possible outcomes)

           = 2 / 8

           = 1 / 4

           = 0.25

So, the probability of adding either ground beef or onion as the first ingredient is 0.25 or 25%.

In this case, we have a total of 8 ingredients, out of which 2 are either ground beef or onion. When selecting the first ingredient, there are 8 possible outcomes. Since we want to calculate the probability of adding either ground beef or onion as the first ingredient, we count the number of desired outcomes, which is 2 (either ground beef or onion). Dividing the number of desired outcomes by the total number of possible outcomes gives us the probability.

The probability of adding either ground beef or onion as the first ingredient is 0.25 or 25%. This means that there is a 25% chance that either ground beef or onion will be the first ingredient added, assuming the ingredients are added randomly without any specific order.

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The standard deviation is 7.35.

Standard deviation is used to determine how the values in a group differs from the mean of the values in the group

In order to determine the standard deviation, take the following steps:

Determine the mean of the observation: (87 + 91 + 74 + 73 + 80 + 84 + 68 + 75) / 8 =79

Determine the difference between each value and the mean and then square the result:

(87 - 79)² + ( 91 - 79) ² + (74 - 79)² + (73 - 79)² + (80 - 79)²  + (84- 79)²  + (68 - 79)²  +( 75- 79) ²

64 + 144 + 25 + 36 + 1 + 25 + 121 + 16 = 432

Determine the mean of the sum of the squared differences and then find the square root of the mean:

√432 / 8 = 7.35

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Answer:

(0,-8)

x=0

y=-8

Step-by-step explanation:

There are a couple of ways you can solve this I used what I think is called the elimination method

We first start by writing the equations in linear form (y=mx+b)

For the first one we have -12x-5y=40

we add 5y to both sides and subtract 40 to get

-12x-40=5y

divide by 5 to get

-12/5x-8=y

Then the second one we have

12x-11y=88

same deal here, add 11y and subtract 88 to get

12x-88=11y

divide by 11 and get

12/11x-8=y

We then set the two equations equal to each other and get

-12/5x-8=12/11x-8

We can add 8 to both sides and get

-12/5x=12/11x

Just by looking at it you can see that the only solution for x is 0

Plug in 0 to the first equation and get -12*0-5y=40

This means that -5y=40

Solve for y and get -8

Answer:

x=0 , y= -8

Step-by-step explanation:

When teaching the client how to use sublingual nitroglycerin (SL NTG) for relief of chest pain at home, the following statements should be included to ensure proper usage and safety.

When instructing the client on the use of sublingual nitroglycerin (SL NTG) for chest pain relief at home, it is essential to cover the following key points:

1. Purpose and indication: Explain that SL NTG is used to relieve angina or chest pain caused by coronary artery disease. Emphasize that it is not meant for prevention but for immediate relief during an episode of chest pain.

2. Proper administration technique: Instruct the client to place the tablet or spray under the tongue and allow it to dissolve or spray it onto or under the tongue. Advise against swallowing or chewing the medication.

3. Dosage and frequency: Specify the appropriate dosage and how frequently the medication can be taken, as prescribed by their healthcare provider. Highlight the importance of following the prescribed dosage and not exceeding the recommended frequency.

4. Response time: Explain that SL NTG acts quickly and should provide relief within a few minutes. Inform the client to seek emergency medical assistance if the chest pain persists or worsens after taking one dose of SL NTG.

5. Storage and expiration: Educate the client on proper storage conditions, such as keeping the medication in its original container, away from light and moisture. Emphasize the importance of regularly checking the expiration date and replacing the medication when it expires.

6. Side effects and precautions: Discuss potential side effects such as headaches, dizziness, and low blood pressure, and advise the client to report any concerning or persistent side effects to their healthcare provider. Stress the importance of informing healthcare providers about the use of SL NTG before undergoing any medical procedures or taking other medications.

7. Emergency instructions: Instruct the client to call emergency services immediately if they experience severe chest pain or if their symptoms do not improve after taking SL NTG.

By providing clear instructions and addressing these important points, the client can effectively and safely use sublingual nitroglycerin for chest pain relief at home. However, it is crucial to consult with a healthcare professional for personalized guidance and to ensure proper usage based on the client's specific medical condition and needs.

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At a price of $44, 30 units of good x are exchanged. This can be calculated by subtracting the quantity supplied at price $15 (q0=10) and the quantity supplied at price $31 (q*=30) from the quantity demanded at price $44 (q1=50).

At a price of $44, the quantity of good x that is exchanged can be calculated by subtracting the quantity supplied at price $15 (q0=10) and the quantity supplied at price $31 (q*=30) from the quantity demanded at price $44 (q1=50). The quantity supplied at price $15 is 10 units, the quantity supplied at price $31 is 30 units, and the quantity demanded at price $44 is 50 units. Therefore, the quantity exchanged at price $44 is 50 units minus 10 units (q0) minus 30 units (q*) which equals 10 units. Thus, the quantity of good x exchanged at price $44 is 10 units.

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Answer:

Step-by-step explanation:

If the missile was going 900 mph and we are trying to find the horizontal velocity

This could be 3.88, and rounding it to the nearest hundredth would be 3.90 miles per minute

Answer:

1.45 miles per minute

Step-by-step explanation:

The question asked it to be presented in miles per minute so divide 1000 by 60 which will give us 50/3. We then multiply that with cos(85) which will give us the final answer of 1.45.

Answer:

\(\cos \theta=-\dfrac{8}{17}\)

Step-by-step explanation:

Coordinates of Point b\(=(-8,15)\)

b lies on the circle whose equation is \(x^2+y^2=289\)

\(x^2+y^2=17^2\)

Comparing with the general form a circle with center at the origin: \(x^2+y^2=r^2\)

The radius of the circle =17 which is the length of the hypotenuse of the terminal ray through point b.

For an angle drawn in standard position through point b,

x=-8 which is negative

y=15 which is positive

Therefore, the angle is in Quadrant II.

\(\cos \theta=\dfrac{Adjacent}{Hypotenuse} \\$Adjacent=-8\\Hypotenuse=17\\\cos \theta=\dfrac{-8}{17} \\\cos \theta=-\dfrac{8}{17}\)

Rounded to the nearest tenth of a foot, the length of KL in triangle KLM is approximately 79.0 feet.

To find the length of KL in triangle KLM, we can use trigonometric ratios based on the given angle measures and side lengths.

Since we know that angle M is a right angle (90°) and angle K measures 85°, we can find the measure of angle L by using the fact that the sum of angles in a triangle is 180°:

∠L = 180° - ∠K - ∠M = 180° - 85° - 90° = 5°.

Now, we can use the trigonometric ratio of tangent (tan) to find the length of KL:

tan ∠K = KL / MK.

Plugging in the known values, we have:

tan 85° = KL / 6.9 feet.

Rearranging the equation to solve for KL, we get:

KL = tan 85° * 6.9 feet.

Using a calculator, we find that tan 85° is approximately 11.43.

Substituting this value into the equation, we have:

KL = 11.43 * 6.9 feet = 78.96 feet.

Rounded to the nearest tenth of a foot, the length of KL in triangle KLM is approximately 79.0 feet.

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Answer:

n \(\leq\) 12

n \(\leq\) 12

20 + 12n \(\geq\) 250 ;

Step-by-step explanation:

#8: In order to eat for free you must be 12 years old or under- including 12 years. So, we can say that you must be less than 12 years old, (n < 12, "n" being your age) OR equal to 12 years old, (n = 12) in order to eat for free. When you combine being able to be less or more than a number but can also be that number you use the "less/greater than or equal to" sign \(\leq\) or \(\geq\) .

#9: The same thing as the #8, the package can be any weight under 12  pounds, but since the limit is 12, the heaviest it can be is also 12.

#10: So we know that Blake needs at LEAST $250. He has $20 already, which is an important part of the inequality. So, as of now, he currently has $20 before mowing lawns.

20 = 250

He needs more money than that, but he's not sure how much which is where the $12 per lawns mowed comes in.

So, "n" is going to be our variable in this inequality. n = the number of lawns he mows. So, if we know he gets $12 for every individual lawn he mows, we can say that he needs an additional $12n in order to afford the $250 headphones.

So now we put what we have together:

12n + 20 = 250

We add the 20 because that's the amount that Blake originally had and we can't forget about it, the 12n is just the additional money he needs in order to reach his $250.

But we're not completely done yet, because if you solve 12n + 20 = 250, it won't give you a nice number, you can't mow exactly 19.16666666666 lawns. So, we're going to say:

12n + 20 \(\geq\) 250

This is saying that the money that Blake ends up making in the end has to be MORE than or EXACTLY $250. We can't use a 'less than equality sign' or 'equal to' sign because you can't buy something for less than what it's worth.

The real rate of interest that you are paying is 3.5%.

The rate of interest, often referred to as the interest rate, is the percentage or proportion of the principal amount that is charged or earned over a certain period of time. It represents the cost of borrowing money or the return on investment. The rate of interest is typically expressed as an annual percentage, but it can also be calculated for shorter or longer time periods depending on the context.

The real rate of interest is calculated by subtracting the inflation rate from the nominal interest rate. In this case, the nominal interest rate is 6.5% per year, and the inflation rate is 3% per year.

Real Rate of Interest = Nominal Interest Rate - Inflation Rate

Real Rate of Interest = 6.5% - 3%

Real Rate of Interest = 3.5%

Therefore, the real rate of interest that you are paying is 3.5%.

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Answer:

can you change this picture?

Answer:

999,960

Step-by-step explanation:

let x be a multiple of 120

120x ≤ 999,999

999,999 / 120 = 8333.325

8333 ≤ x ≤ 8334

8333(120) = 999,960

8334(1200) = 1,000,080  this is a 7-digit number

Therefore, the largest 6-digit number that is exactly divisible by 120 is 999,960

Answer:

V = s³

Step-by-step explanation:

You multiply all sides together (L×W×H)

Multiply everything to get 90, because for every option, you multiply that one with the other.

Answer: maybe like 5

Step-by-step explanation:

Answer:

x < 2

Step-by-step explanation:

1. Isolate x by adding 25 to both sides: 5x < 10

2. Divide both sides by 5: x < 2

Answer:  $81.60

Step-by-step explanation:

Bill: $68.00

Tip: $13.60

Total: $81.60

Answer:

81.60

Step-by-step explanation:

Find the total amount of the bill

First, determine the amount of the tip

68 * 20%

68 * .2

13.60

Add this to the bill

68 + 13.6

81.60

Answer: each store gets 787 pairs and 1 is left over

Step-by-step explanation:Divide 4723 by 6

The equation of the line that passes through the points (−8, −10) and (6, 3)

The slope, m of the linear function is calculated using the points (−8, −10) and (6, 3)

m = (y₀ - y₁) / (x₀ - x₁)

m = (-10 - 3) / (-8 - 6)

m = (-13) / (-14)

m = 13/14

equation passing through point (6, 3) using the point slope formula

(y - y₁) = m'  (x - x₁)

y - 3 = 13/14(x - 6)

y - 3 = 13/14 x - 39/7

y = 13/14 x - 39/7 + 3

y = 13/14 x - 18/7

The equation of the line in slope intercept form is y = 13/14 x - 18/7

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Answer:

e = -2

Step-by-step explanation:

Hey man, I got straight A's in math all year so here's the answer!

Good Luck! :)

Answer:

x = 4

Step-by-step explanation:

Given

2x² - 7x - 4

To solve for x , equate the expression to zero

2x² - 7x - 4 = 0 ← in standard form

(x - 4)(2x + 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = - \(\frac{1}{2}\)

Thus the positive value of x is x = 4

Answer:

x=4

Step-by-step explanation:

Hope this helped have an amazing day!  

The first partial derivative with respect to x is 4x^3 + 4y^9, and the first partial derivative with respect to y is 36xy^8.

To find the first partial derivatives of the function f(x, y) = x^4 + 4xy^9, we differentiate the function with respect to each variable separately.

Taking the partial derivative with respect to x (denoted as ∂f/∂x):

∂f/∂x = 4x^3 + 4y^9

Taking the partial derivative with respect to y (denoted as ∂f/∂y):

∂f/∂y = 36xy^8

Therefore, the first partial derivative with respect to x is 4x^3 + 4y^9, and the first partial derivative with respect to y is 36xy^8.

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