Practice Question: Solve: 3x + y = 8 3x² + y² = 28​

Answer:

6

Step-by-step explanation:

Using the formula for velocity of money:

Velocity of money = (Price level x Real output) / Money supply

Plugging in the given values, we get:

Velocity of money = (120 x 300 billion) / 6 trillion

Velocity of money = 6

Therefore, the velocity of money is 6.

Answer:

Since we are given that the railing will begin at a height of 36 inches and follow the slant of the stairs, which decreases 9 vertical inches for every 12 horizontal inches.

Thus the rate of change :  

Rate of change represents the slope of line.

Since we are given that height, y, of the railing in inches according to the horizontal distance in inches, x, from the top of the stairs

And the initial height of the railing was 36 inches .

So,the function which would represent the situation can be shown using equation of line :

y = mx+c

So

c = 36 inches

So, the function :

Hence The function which can represent the height, y, of the railing in inches according to the horizontal distance in inches, x, from the top of the stairs :

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*Keyword:

Slope, proportion, relationship, decrease, line equation

The key to answering this question is to understand what means that the height of the railing decreases 9 vertical inches per 12 inches horizontal. This ratio represents the slope of the railing and therefore the slope of the line equation. We can write the relationship as follows:

Step-by-step explanation:

Answer:

y = –3/4 x + 36

Step-by-step explanation:

took the quiz

Answer:

No, but if it was how many studens school like math then yes

in Step-by-step explanation:

A Möbius transformation is a transformation of the form f(z) = (az+b)/(cz+d), where a, b, c, and d are complex numbers and ad-bc ≠ 0. The complex number z maps to f(z).

To find the Möbius transformation f such that f(0) = 0, f(1) = 1, f([infinity]) = 2, we follow these steps:

Step 1: Map 0 to 0 We need to map 0 to 0, so we set f(0) = 0. So, we get 0 = (a(0) + b) / (c(0) + d). This gives us b = 0. Step 2: Map infinity to 2We need to map [infinity] to 2, so we set f([infinity]) = 2. So, we get 2 = (a[infinity] + b) / (c[infinity] + d). This gives us a/c = 2/d. Cross-multiplying the terms, we get ad = 2c.

Let us assume that d = 1, then we have a = 2c.

We can substitute this value of a in the Möbius transformation, and we get f(z) = (2cz) / (cz + 1).Step 3: Map 1 to 1To map 1 to 1, we evaluate the Möbius transformation at z = 1. We get f(1) = (2c) / (c + 1) = 1.

Solving this, we get c = -1/2. Therefore, the Möbius transformation is f(z) = (2z) / (z - 2).

Hence, we have found the required Möbius transformation f(z) = (2z) / (z - 2) such that f(0) = 0, f(1) = 1, and f([infinity]) = 2.

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Answer:

Option 4: DF ≅ DE

Step-by-step explanation:

Triangle DEF is an isosceles triangle with two sides of equal length and EF is the hypotenuse.

The length of the pipe required would be 31.06 meters

The length of the pipe is the hypotenus of the triangle formed :

substituting the values into our equation:

length of pipe = √17² + 26²

length of pipe = √965 = 31.06

Therefore, the length of the pipe needed is 31.06 meters

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The set of numbers from least to greatest is-

5×10⁻², 6%, 2/5, 4/9, 2⁻¹, √3.

For the given numbers;

The given number are-

2/5, 5×10⁻², √3, 6%, 4/9, 2⁻¹.

These number can be written in the decimal form as;

Now arrange the number from least to greatest.

0.058, 0.06, 0.40, 0.44, 0.5, 1.73

Convert the number in given form.

5×10⁻², 6%, 2/5, 4/9, 2⁻¹, √3.

Thus, the number represented in the ascending order are-

5×10⁻², 6%, 2/5, 4/9, 2⁻¹, √3.

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With a small sample size (n=9), the condition of the population distribution being approximately normal becomes more important to ensure the validity of the Central Limit Theorem. The standard error of the sampling distribution of sample means is approximately $4.33 (rounded to 2 decimal places).

a. The Central Limit Theorem states that for a large enough sample size, the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the population distribution.

However, with a small sample size (n=9), the condition of the population distribution being approximately normal becomes more important to ensure the validity of the Central Limit Theorem.

b. The standard error of the sampling distribution of sample means can be calculated using the formula:

Standard Error (SE) = Standard Deviation / Square Root of Sample Size

We have that the population standard deviation is $13 and the sample size is 9, we can calculate the standard error:

SE = $13 / √9

  = $13 / 3

  ≈ $4.33

Therefore, the standard error of the sampling distribution of sample means is approximately $4.33 (rounded to 2 decimal places).

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The experiment will end after 4th time.

hence, after 4th  trial experiment will stop.

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The average stopping distance when driving at 55 mph on dry, level pavement can vary depending on several factors such as vehicle condition, road conditions, and driver reaction time.

Therefore, it is not possible to provide an exact average stopping distance without more specific information.

However, as a general guideline, it is commonly recommended to use the "3-second rule" for following distance. This means that you should maintain a distance from the vehicle in front of you that would allow you to come to a complete stop within three seconds. At higher speeds like 55 mph, the stopping distance will be longer compared to lower speeds.

To estimate the average stopping distance, you can consider the total stopping distance, which is the sum of the perception distance, reaction distance, and braking distance. The perception distance is the distance your vehicle travels while you recognize a need to stop, the reaction distance is the distance traveled during your reaction time, and the braking distance is the distance covered while your vehicle comes to a stop after applying the brakes.

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that would be 33 square feet!!!

The total e-waste generated over these two years in the region, expressed in scientific notation, is B. 2.49 x 10^7 tons.

Scientific notation is a standard form of expressing a short or large number in a decimal form.

Scientific notation involves writing a number that is greater than 1 but less than 10 with the power of 10.

Correct scientific notations express numbers as products of a number between 1 and 10 multiplied by an appropriate power of 10 based on its place value in the given decimal.

Thus, the total e-waste generated cannot be expressed in scientific notation as Options A, C, or D because these do not comply with the rules of scientific notations, unlike Option B.

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the requried length and width of the pool can be given by the expression l = 38.5 - w.

Let's use algebra to solve this problem. Let's call the length of the pool "l" and the width of the pool "w". We know that the perimeter of a rectangle is given by:

Perimeter = 2l + 2w

2l + 2w = 77

l + w = 38.5

l = 38.5 - w

Thus, the requried length and width of the pool can be given by the expression l = 38.5 - w.

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Answer:

39.

Step-by-step explanation:

(15 ÷5) + 9 + (14 - 5 ) x 3

= 3 + 9 + 9 x 3

= 3 + 9 + 27

= 39.

The area of the hexagon is 1374.4 square cm.

A hexagon has a radius measuring 23 cm.

What is the approximate area of the hexagon?

A hexagon has a radius measuring 23 cm.

Regular hexagons have six equal sides and six angles and are composed of six equilateral triangles.

\(\rm Area = \dfrac{3\sqrt{3}}{2}s^2\)

Where, s is the radius of the hexagon.

Then,

The area of the hexagon is,

\(\rm Area = \dfrac{3\sqrt{3}}{2}s^2\\ \\ \rm Area = \dfrac{3\sqrt{3}}{2}(23)^2\\ \\ \rm Area = \dfrac{3\sqrt{3}}{2} \times 529\\ \\ \rm Area = 3\sqrt{3}} \times 264.5\\ \\ Area = 5.19 \times 264.5\\ \\ Area = 1374. 4 \ square \ cm\)

Hence, The area of the hexagon is 1374.4 square cm.

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Answer:

Area of the hexagon is 1374.4 cm

Step-by-step explanation:

Edge

Answer:

bro, i answered it already

in your previous question

the second 133.40

To find coterminal angles, you have to either add or subtract 2π. In this case, you would use 8π/4 so there is a common denominator.

Positives:

-3π/4+8π/4 = 5π/4

5π/4+8π/4 = 13π/4

Negative:

-3π/4-8π/4 = -11π/4

-11π/4-8π/4 = -19π/4

In geometry, an angle measure is the length of the angle formed by two rays or arms intersecting at a common vertex.

Using a protractor, angles are measured in degrees (°). Joseph Huddart created the protractor in 1801. It was a more sophisticated protractor.

The angle created at the center of a circle is measured in radians, the unit of angular measurement. It is described as an angle that subtends from a circle's center and intercepts at an arc with a radius equal to the circle's radius. 57.3° is equal to one radian.

Acute angle, Obtuse angle, Right angle, Straight angle, reflex angle, and full rotation are the names of basic angles.

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Answer:

31.35%

Step-by-step explanation:

In the box, there are:

Total number of pens in the box = 6 + 4 + 7

= 17

If we count pens as outcomes the total number of possible outcomes are 17.

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Clarissa takes out a black pen from the box.

That reduces the number of black pens by 1 which increases the total number of pens by 1 as well.

So now:

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

\( \boxed{ \mathsf{probability = \frac{favorable \: outcomes}{total \: outcomes} }}\)

If we want her to pick up a black pen, and she ends up picking one. So, we can say that the outcome is in our favor.

That makes it,

= 5

= 16

\( \implies\mathsf{probability = \frac{5}{16} }\)

For showing it as some percent we'll just multiply the fraction by 100

\( \implies \mathsf{ \frac{5}{16} \times 100 }\)

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

\( \implies \mathsf{ \underline{ 31.25 \: \% } }\)

Answer:

81.9

Step-by-step explanation:

simple math  pls mark brainlist

Answer:

solution set={35/3}

Step-by-step explanation:

--3(x+5)=50

3x+15=50

3x+15-15=50-15

3x=35

3x/3=35/3

x=35/3=11.66

solution set={35/3}

hope it will help ^_^

Answer:

????

Step-by-step explanation:

thththtthththt

Answer:

V= 68.6 m/s

Step-by-step explanation:

height above the ground t seconds after it is dropped is 675-4.9t^2

For seven seconds

Height above ground= 675-4.9(7)²

height above ground= 675-240.1

Height above ground= 434.9 m

But it's dropped from a cliff and we need to find the distance traveled from the too of the cliff

Distance= 675-434.9.

Distance= 240.1

To determine it's speed

V²= U² +2gs

V= velocity we are looking for

U= initial velocity= 0

G= acceleration due to gravity= 9.8 m/s²

s= distance covered

V²= U² +2gs

V²= 0+2(9.8)(240.1)

V²= 4705.96

V= 68.6 m/s

Answer:

18

Step-by-step explanation:

The given information indicates that the average speed on the 405 freeway follows a normal distribution with a mean of 50 mph and a standard deviation of 12 mph. To find the probability that someone is driving slower than 35 mph, we need to calculate the deviation from the mean using the z-score formula:

z = (x - μ) / σ

where x is the value we are interested in (35 mph), μ is the mean (50 mph), and σ is the standard deviation (12 mph).

z = (35 - 50) / 12
z = -1.25

Using a standard normal distribution table or calculator, we can find the probability that a z-score is less than -1.25. The probability is approximately 0.1056 or 10.56%.

Therefore, the probability that someone is driving slower than 35 mph on the 405 freeway is about 10.56%.

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The increase in equilibrium GDP would be 125.

To calculate the increase in equilibrium GDP when planned investment increases from 20 to 45, we need to consider the multiplier effect. The multiplier is determined by the marginal propensity to consume (MPC), which is the fraction of each additional dollar of income that is spent on consumption.

In this case, the consumption function is given as C = 357 + 0.8Y, where Y represents GDP. The MPC can be calculated by taking the coefficient of Y, which is 0.8.

The multiplier (K) can be calculated using the formula: K = 1 / (1 - MPC).

MPC = 0.8

K = 1 / (1 - 0.8) = 1 / 0.2 = 5

The increase in equilibrium GDP (∆Y) is given by: ∆Y = ∆I * K, where ∆I represents the change in planned investment.

∆I = 45 - 20 = 25

∆Y = 25 * 5 = 125

Therefore, the increase in equilibrium GDP would be 125.

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Answer:

11 meters, 4.1 centimeters

Step-by-step explanation:

If for every centimeter it equals 2 meters, we can use this expression to solve for the width of the building in real-life:

Therefore, the width of the building is 11 meters in real life.

If the real-life height of the building is 8.2 m tall, then we can use this expression:

Because we were given the drawings width the first time, we needed to multiply by 2 to get the real-life height in meters. But now that we are given the real-life height, we now need to divide by 2 to get the height of the drawing in centimeters.

Therefore, the width, in meters, of the building in real life is 11 meters, and the height of the drawing is 4.1 centimeters.

Answer:

0.27 is the unit rate

The account balance after 3 years with continuous compounding at an interest rate of 3% will be approximately $5,142.62.

The formula accrued amount compounded continuously is expressed as;

\(A = P\ *\ e^{rt}\)

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given that:

Principal P = $4,700

Compounded contiously

Time t = 3 years

Interest rate r = 3%

Accrued amount A = ?

First, convert rate R as a percent to r as a decimal

r = R/100

r = 3/100

r = 0.03

Plug these values into the above formula and solve for accrued amount.

\(A = P\ *\ e^{rt}\\\\A = 4,700\ *\ e^{(0.03\ *\ 3) }\\\\A = 4,700\ *\ e^{(0.09) }\\\\A = 5,142.62\)

Therefore, the accrued amount is $5,142.62.

Option A) $5,142.62 is the correct answer.

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The given matrices are a 3x2 matrix and a 2x1 matrix, which means they can be multiplied. To perform the multiplication, we need to multiply the corresponding elements in each row of the first matrix with the corresponding elements in each column of the second matrix and add the products.

The resulting matrix will be a 3x1 matrix, which means it will have 3 rows and 1 column.

Performing the multiplication, we get:
[7 -5]   [1]    [(7x1) + (-5x2)]   [(-5)]
[2 -9] x [2]  = [(2x1) + (-9x2)] = [-16]
[1 -3]   [10]   [(1x1) + (-3x2)]   [-17]
Therefore, the resulting matrix is:
[ 1 ]
[-16]
[-17]
So, the answer to the given problem is:
[ 1 ]
[-16]
[-17]

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