The weight of an object on Mars varies directly with its weight on Earth. An object that weighs 50 pounds on Mars weighs 150 pounds on Earth. Determine a direct variation equation to represent this situation. If an object weighs 120 pounds on Earth, determine how much an object would weigh on Mars. Enter this amount, in pounds, into the space provided (enter numerical number only, not the units).

The features of the function g(x) = f(x + 4) + 8 are:

To analyze the features of the function g(x) = f(x + 4) + 8, we need to consider the effects of each transformation applied to the original function f(x) = log2 x.

Translation: f(x + 4)

This transformation shifts the graph of f(x) horizontally to the left by 4 units. It means that every x-coordinate in f(x) is decreased by 4 units.

Vertical Shift: f(x + 4) + 8

After the horizontal translation, the graph is shifted vertically upward by 8 units. This means that every y-coordinate in f(x + 4) is increased by 8 units.

Based on these transformations, we can identify the features of the function g(x):

Y-intercept: The y-intercept of the function g(x) = f(x + 4) + 8 is (0, 10). This means that the graph intersects the y-axis at the point (0, 10).

Domain: The domain of the function g(x) = f(x + 4) + 8 is (4, ∞). The original function f(x) = log2 x has a domain of (0, ∞), but after the horizontal translation of 4 units to the left, the new domain starts from x = 4.

Range: The range of the function g(x) = f(x + 4) + 8 is (8, ∞). The original function f(x) = log2 x has a range of (-∞, ∞), but after the vertical shift of 8 units upward, the new range starts from y = 8.

Vertical Asymptote: The vertical asymptote of the function g(x) = f(x + 4) + 8 is x = -4. This vertical asymptote is the result of the original function f(x) = log2 x having a vertical asymptote at x = 0. After the horizontal translation of 4 units to the left, the asymptote also shifts 4 units to the left and becomes x = -4.

X-intercept: The x-intercept of the function g(x) = f(x + 4) + 8 is (1, 0).

This means that the graph intersects the x-axis at the point (1, 0).

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Answer:

C) 23

Step-by-step explanation:

If the computer monitor is 20 inches wide, and 12 inches high, we can solve for the diagonal by using the Pythagorean theorem.

Let a = the width, let b= the height, let c = the diagonal.

a^2 + b^2 = c^2

20^2 +12^2 =c^2

400 + 144 = c^2

544 = c^2

C is approximately equal to 23 inches.

Let me know if this helps!

The simplified form of the given expression is 41.216.

The given expression is (3.2)(3.22)4.

We have to solve the given expression.

We can solve this equation by multiplying the term to one another because we know that if there is no symbol between the term then there should be the symbol of multiplication.

So we can write the given expression as

(3.2) × (3.22) × 4

To simplify this expression we first multiply the 3.2 to the 3.22 or we can also multiply 3.2 to the 4 or we can also multiply 3.22 to the 4. After multiplying the two term then we multiply the result of two number multiplication to the third number.

In that way we can easily simplify the given expression. Now,

= 10.304 × 4

= 41.216

Hence, the simplified form of the given expression is 41.216.

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In order to write a function myMedian that takes a vector as input and returns the median of the vector as output, we can follow these steps:

Step 1: Define a function named myMedian that takes a vector as input.

Step 2: Sort the elements of the vector in ascending order.

Step 3: Find the length of the vector.

Step 4: If the length of the vector is even, then calculate the average of the middle two elements.

Step 5: If the length of the vector is odd, then return the middle element.

Step 6: Display the median of the vector as output. We can use the myMedian function in the command window and verify the result by comparing with the output of the built-in function median.

Here's the code for the function myMedian in MATLAB:

```function med = myMedian(vector)
 sortedVector = sort(vector);
 n = length(sortedVector);
 
 if mod(n, 2) == 0
   med = (sortedVector(n/2) + sortedVector(n/2 + 1)) / 2;
 else
   med = sortedVector((n+1)/2);
 end
 
end```

To verify the output, we can run the following code in the command window:```
v = [2, 5, 1, 7, 3];
m1 = myMedian(v) % output should be 3
m2 = median(v) % output should be 3

```Here, we have created a vector v and passed it to the myMedian function. We have stored the output in m1 variable. We have also used the built-in median function to calculate the median of the vector v and stored it in m2 variable. Finally, we have displayed both the medians and compared them. They should be equal.

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The approximate surface-area-to-volume ratio of a bowling ball with a radius of 5 inches is 0.6

To find the approximate surface-area-to-volume ratio of a bowling ball with a radius of 5 inches, we will first calculate the surface area (SA) and volume (V) of the ball, and then divide the surface area by the volume.

Step 1: Calculate the surface area (SA) using the formula for the surface area of a sphere:

\(SA = 4 πr^2\)
\(SA = 4 π5^2\)
\(SA = 4 π(25)\)
\(SA=100π\)

Step 2: Calculate the volume (V) using the formula for the volume of a sphere:

\(V = \frac{4}{3} π (r)^{3}\)
\(V = \frac{4}{3} π (5)^{3}\)
\(V = \frac{4}{3} π (125)\)
V = 166.67 π cubic inches

Step 3: Calculate the surface-area-to-volume ratio (SA/V)
\(\frac{SA}{V} = \frac{100}{166.67}\)
\(\frac{SA}{V}=\frac{100}{166.67}\)

\(\frac{SA}{V}= 0.6\)

So the approximate surface-area-to-volume ratio of a bowling ball with a radius of 5 inches is 0.6. The best answer from the choices provided is A.

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Answer:

The height is 7 inches

Step-by-step explanation:

Given

\(Base\ Area = 15in^2\)

\(Volume = 105in^3\)

Required

Determine the height [missing from the question]

The volume of a hexagonal prism is:

\(Volume = Base\ Area * Height\)

Make Height the subject

\(Height = \frac{Volume}{Base\ Area}\)

\(Height = \frac{105in^3}{15in^2}\)

\(Height = \frac{105in}{15}\)

\(Height = 7in\)

Answer:

I like ur hand writing im trying to answerur question!

Answer:

30 and 16

Step-by-step explanation:

x + y = 46

14 + y + y = 46

14 + 2y = 46

2y = 32

y = 16

Now we know y is 16. Which means that we can substitute y for 16 in equation A and solve for x:

x + y = 46

x + 16 = 46

X = 30

Answer:

780 flaps per second

Step-by-step explanation:

just multiply 13×60

The volume of the cube expressed as a fraction will be 27x³y³ / 64.

Given that:

Volume, V = (0.75xy)³

It is frequently mathematically quantified using SI-derived units or different imperial or US traditional units. The concept of length is linked to the notion of capacity.

The volume of the cube expressed as a fraction is calculated as,

V = (0.75xy)³

V = (3xy/4)³

V = 27x³y³ / 64

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If you make annual payments of $1400 for 8 years at a 6% interest rate compounded annually, the total amount accumulated over the 8-year period would be approximately $12,350.

To explain further, when you make annual payments of $1400 for 8 years, you are essentially depositing $1400 into an account each year. The interest rate of 6% compounded annually means that the interest is added to the account balance once a year.

To calculate the total amount accumulated, you can use the formula for the future value of an ordinary annuity:

FV = P * ((1 + r)^n - 1) / r

where FV is the future value, P is the payment amount, r is the interest rate per compounding period (in this case, 6% or 0.06), and n is the number of compounding periods (in this case, 8 years).

Plugging in the values, we have:

FV = $1400 * ((1 + 0.06)^8 - 1) / 0.06

≈ $12,350

Therefore, the total amount accumulated over the 8-year period would be approximately $12,350.

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Hey!!!

Here's your answer

-9*4=-36

So the right answer -36.

Hope it will help you

Good luck on your assignment

Answer:

-36

Step-by-step explanation:

-9*4 = -(9*4) = -36

Answer:

it's d

.

hope I helped! I need to write more words so I can send this

Answer:

The answer is A

Step-by-step explanation:

|6x + 3| = 27

6x + 3 = 27

6x + 3 = -27

6x = 24

6x = -30

x = 4

x = -5

So:

x = 4, -5

Answer:

Step-by-step explanation:

first one

Answer:

c)3pi/4

Step-by-step explanation:

17) The proof that LKMN is a parallelogram is given as follows:

18) Given that ∠W is the midpoint of Line SU: Line ST || VU, the proof that STUV is a parallelogram is:

Proof is a stringent mathematical argument that establishes the truth of a certain claim clearly. A theorem is a mathematical assertion that has been demonstrated.

Mathematicians disagree over what exactly constitutes a proof. This dispute is shown by the four-color theorem, whose "evidence" is based on intensive computer testing of numerous specific examples that cannot be checked "by hand." While many mathematicians consider computer-assisted proofs to be legitimate, some purists disagree.

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The missing angles of the Triangle are; ∠1 = 62°; ∠2 = 45° and ∠3 = 22°.

We know that the sum of angles on a straight line is 180 degrees. Thus, we can say that;

∠1 + 118° = 180°

∠1  = 180 - 118

∠1 = 62°

We also know that sum of angles in a triangle is equal to 180°. Thus;

∠1 + ∠2  + 73 = 180

Plugging in the relevant value gives;

62 + ∠2  + 73 = 180

∠2 = 180 - 135

∠2 = 45°

∠2 + ∠3 = 180 - (∠1 + 49)

∠2 + ∠3 = 180 - (62 + 49)

45° + ∠3 = 69

∠3 = 22°

Thus, we conclude that the missing angles of the Triangle are; ∠1 = 62°; ∠2 = 45° and ∠3 = 22°.

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Answer:

=17x²-x

Step-by-step explanation:

=x.(9x²+18x-x-2)-x.(9x²-1)

=x.(9x²+17x-2-9x²+1)

=x.(17x-1)

=17x²-x

To convert an expression into standard form a + bi, you separate the real and imaginary parts and combine them using the appropriate operators.

To write an expression into standard form, a + bi form, you need to separate the real and imaginary components of the expression and combine them using the appropriate notation.

In a + bi form, 'a' represents the real part of the expression, and 'b' represents the imaginary part.

Let's say we have an expression in the form x + yi, where 'x' is the real part and 'y' is the imaginary part.

To convert this expression into standard form, you need to perform the following steps:

Separate the real and imaginary parts of the expression.

Write the real part first, followed by the imaginary part with 'i'.

Combine the real and imaginary parts using the appropriate operators (+ or -).

Let's take an example to illustrate this process:

Suppose we have the expression 3 + 2i.

Here, '3' is the real part, and '2' is the imaginary part.

To convert it into standard form, we write it as 3 + 2i.

Similarly, if we have the expression -5 - 4i, where '-5' is the real part and '-4' is the imaginary part, we write it as -5 - 4i.

In both cases, the expressions are in standard form, a + bi.

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Answer:

$87.5

Step-by-step explanation:

Original price also means COST PRICE

C.P=$50

S.P=75% of $50-$50

To find the sale price it will be 75% of C.P -C.P

75% × $50 + $50= 0.75 × $50-$50

=$37.5-$50.

= $12.5

therefore the sale price is $12.5

THANK YOU

The price of the sweatshirt at the sale is $12.5 which is 75% off of the original price.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, The original price of a sweatshirt is $50.

Also given that the sale price is 75% off the original price So, the cost of the sweatshirt is (100 - 75)% = 25% of the original price which is,

= (25/100)×50.

= $12.5.

So, The sale price of the sweatshirt is $12.5.

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Maclaurin polynomial p3(x) for f(x) = e^(4x) is given by p3(x) = 1 + 4x + 8x^2 + 16x^3. This polynomial serves as an approximation of the function e^(4x) near x = 0.

The Maclaurin polynomial p3(x) for the function f(x) = e^(4x) is a polynomial approximation centered at x = 0 that uses up to the third degree terms.

The Maclaurin series expansion is a special case of the Taylor series expansion, where the center of the approximation is set to zero. By taking the derivatives of f(x) and evaluating them at x = 0, we can determine the coefficients of the polynomial.

To find p3(x), we start by calculating the derivatives of f(x). The derivatives of e^(4x) are 4^n * e^(4x), where n represents the order of the derivative.

Evaluating these derivatives at x = 0, we find that f(0) = 1, f'(0) = 4, f''(0) = 16, and f'''(0) = 64. These values become the coefficients of the respective terms in the Maclaurin polynomial.

Therefore, the Maclaurin polynomial p3(x) for f(x) = e^(4x) is given by p3(x) = 1 + 4x + 8x^2 + 16x^3. This polynomial serves as an approximation of the function e^(4x) near x = 0, where the accuracy improves as more terms are added.

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Answer:

9

Step-by-step explanation:

total is 30

spent is $9

this is total money minus the amount of the picture frame

30-9

21 divide by 3

the total sum of journals bought was 9

Answer:

See below

Step-by-step explanation:

Geometric sequences have a common ratio while arithmetic sequences have a common difference.

On the left table, we can see that it's an arithmetic sequence because 3+2=5, 5+2=7, and so on.

On the right table, we can see that it's a geometric sequence because 3*2=6, 6*2=12, and so on.

Basically, if you see a multiplication pattern for the output, it's a geometric sequence. If you see an addition (or subtraction) pattern for the output, it's an arithmetic sequence

Answer:

umm can you tell us the options then I can say what the answer is and I'll edit or put it in the comments

Step-by-step explanation:

have a good rest of your day tho :) ❤

Answer:

440

Step-by-step explanation:

Answer:

63,384

Step-by-step explanation:

The explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

The given sequence is -4, 16, -64, 256,...

If we observe the sequence it is a geometric sequence

aₙ=a.rⁿ⁻¹

a is the first term and r is the common ratio

From the sequence the first term is -4 and common ratio is -4

aₙ=(-4).(-4)ⁿ⁻¹

Plug in the value n as 8

a₈=(-4).(-4)⁷

The value of minus four power seven is minus sixteen thousand three hundred eighty four

a₈=(-4)(-16384)

When four is multiplied with sixteen thousand three hundred eighty four we get sixty five thousand five hundred thirty six

a₈= 65536

Hence, the explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

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Answer:

\( \frac{ - 1}{2} \)