If you vertically compress the exponential function f(x)=2^x by a factor of 5, what is the equation of the new function?

Based on the fact that Ram bought some pens and they cost Rs.90 but if he had paid Rs.1 less for each he would have 3 more pens, the number of pens he bought is 6 pens.

This can be represented as:

(x + 3) (y - 3) = 90

Where xy = 90

xy - 3x + 3y - 9 = xy

3y - 3x - 9 = 0

y - x - 3 = 0

x - y + 3 = 0

Solving further gives:

x - 90/ x + 3 = 0

x² + 3x - 90 = 0

Remembering that:

90 = 9 x 10

= 3 x 3 x 2 x 5

= 15 x -6

Going back to the formula:

x (x + 15) - 6 (x + 15)

(x + 15) (x - 6) = 0

x - 6 = 0

x = 6 pens

In conclusion, the number of pens bought was 6 pens.

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Answer:

A

Step-by-step explanation:

If you were to substitute 2 or -3 into equation A, the denominator would be zero and you would have to divide by zero. Thus there are asymptotes for this function at -3 and 2, matching the graph

Answer:

See below

Step-by-step explanation:

GCF (greatest common factor ) of 42 and 30   is  6

  each row will have 6 seedlings

     there will be  (  42+30) / 6 = 12 rows

                   7 pine rows    5 juniper rows

5+a-4√(a+1)/(a-3) is the simplified form of the number. This can be obtained by multiplying numerator and denominator with conjugate of the denominator.

Given the number,

√a+1-2/√a+1+2

Denominator = √a+1+2

Conjugate of the denominator = √a+1 - 2

Now, (√a+1-2)(√a+1 - 2 )/√(a+1+2)(√a+1 - 2 )

=(√a+1 - 2 )²/(√a+1)² - 4

=(a+1 -4√a+1+5)/(a+1-4)

=5+a-4√(a+1)/(a-3)

Hence 5+a-4√(a+1)/(a-3) is the simplified form of the number.

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Answer:

y = 21

Step-by-step explanation:

When x is directly proportional to y:

When x increases, y also increases.

In this case, it is so you write,

1. Write down the formula: y=kx

k being the constant.

Let's use "When x = 4, y = 7" to work out the constant.

2. Substitute the 'when' values: 7=k×4

3. Rearrange to find the constant: 7÷4=k

4. Find k: k=1.75

Now let's see the new problem, 'what is y when x = 12'.

5. Substitute the values now but keep the constant: y = 1.75 × 12

6. Rearrange if needed.

7. Find the missing value: y = 21

Hope this helped and if you require further assistance from me please comment below! :)

Ps: If it was inversely proportional then the formula would be y = k / x

with k still being the constant.

Answer:

$4.50

Step-by-step explanation:

Okay so, first add both.

50+40 is 90, then multiply 90 by the tax percent which is

90x5%=4.5

If expression then,

x=money that they have to pay.

5%(50+40)=x    (the original)

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The value of angle 20 is as follows:

m∠20 = 50.9 degrees.

When parallel lines are cut by a transversal, angle relationships are formed. This include corresponding angles, alternate angles , vertical angles etc.

Therefore, line l and m are parallel lines cut by the two transversal.

Hence,

m∠6 ≅ m∠20 (alternate angles)

Therefore, alternate angles are congruent

m∠20 = 2x - 4

m∠19 + m∠20 = 180 (angles on a straight line)

5x - 8 + 2x - 4 = 180

7x - 12 = 180

7x = 180 + 12

7x = 192

x = 192 / 7

x = 27.4285714286

x = 27.43

Therefore,

m∠20 = 2(27.43) - 4

m∠20 = 50.8571428571

m∠20 = 50.9 degrees.

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Answer:

The temperature was 3 degrees colder in the afternoon

Step-by-step explanation:

numbers on the left of zero on the number line are arranged in decreasing order and as such -2 is greater than -5.

The true statement is The temperature was 3 degrees colder in the afternoon.

Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.

Given that, Darcy read her thermometer in the morning and the temperature was -2° C. In the afternoon, the same thermometer showed a temperature of -5° C.

-2-3 = -5

We see, that, the temperature is falling from -2 to -5, that means, there was a fall in temperature from morning to afternoon.

Hence, the temperature was 3 degrees colder in the afternoon.

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The value of r If r varies directly with the square of m and inversely with s is 240

Suppose r varies directly with the square of m and inversely with s.

If r varies directly with the square of m and inversely with s, then;

r = km²/s

Given that R = 15 when m = 6 s= 4

15 = k(6)²/4

60 = 36k

k = 60/36

k = 5/3

If the value of m = 24 and s = 4, hence;

r = 5/3*24²/4

r = 240

Hence the value of r If r varies directly with the square of m and inversely with s is 240

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The computation shows that the salesman that has the highest total earnings for the three weeks period will be salesman A.

It should be noted that from the information given, we are given the information about three salesmen and their sales.

The total earnings for salesman A will be:

= (1300 × 3) + 65 × (11 + 14 + 16)

= 3900 + 2730

= 6630

The total earnings for salesman B will be:

= 300 × 3 + 40 × (14 + 15 + 13)

= 900 + 1680

= 2580

The total earnings for salesman C will be:

= 900 × 3

= 2700

Therefore, the computation shows that the salesman that has the highest total earnings for the three weeks period will be salesman A.

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Answer:

A. the adult human

B. the adult human

Step-by-step explanation:

A. There are 60 minutes in an hour, and the human's heart beats 72 bpm (beats per minute). If you multiply 60 by 72, you get 4,320 bpm. If you multiply 60 by 35, you only get 2,100 bpm.

B. If you use the same logic that 72 is greater than 35, than you can assume that the human hear makes 1,000,000 beats in less time. However, if you want to do the math, then simply divide 1,000,000 by 72. Then, divide 1,000,000 by 35. Whichever has the smaller number is the one that can make more heart beats in a faster time.

g(x) is a translation of f(x), we have:

g(x) = f(x) - 3

We have the two functions:

[tex]g(x) = x^2 - 3\\\\f(x) = x^2[/tex]

We can see that g(x) is just a translation of 3 units downwards of f(x), to write g(x) in terms of f(x) we can just replace the first term by f(x):

[tex]g(x) = x^2 - 3 = f(x) - 3[/tex]

So we have:

g(x) = f(x) - 3

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The fraction of students that play basketball is  [tex]\mathbf{= \dfrac{1}{10}}[/tex].

The fraction of students that play basketball from the given information can be determined by assuming that the whole number of students in the middle school is whole i.e. (1)

Let us first determine the number of students that participate in sports, we have:

[tex]\mathbf{=1- \dfrac{3}{5}}[/tex]

[tex]\mathbf{= \dfrac{2}{5}}[/tex]

If 1/4 of these students play basketball, then we have:

[tex]\mathbf{= \dfrac{1}{4}\times (\dfrac{2}{5})}[/tex]

[tex]\mathbf{= \dfrac{1}{10}}[/tex] students play basketball.

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The area between the two functions is 0

The functions are given as:

f₁(x)= 1

f₂(x) = |x - 2|

x ∈ [0, 4]

The area between the functions is

A = ∫[f₂(x) - f₁(x) ] dx

The above integral becomes

A = ∫|x - 2| - 1 dx (0 to 4)

When the above is integrated, we have:

A = [(|x - 2|(x - 2))/2 - x] (0 to 4)

Expand the above integral

A = [(|4 - 2|(4 - 2))/2 - 4] - [(|0 - 2|(0 - 2))/2 - 0]

This gives

A = [2 - 4] - [-2- 0]

Evaluate the expression

A = 0

Hence, the area between the two functions is 0

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Answer:

(-2, 6)

Step-by-step explanation:

3x - 4y = -32

3x + 5y = 24

-9y = -56

y = [tex]\frac{56}{9}[/tex] = 6

3x - 4*[tex]\frac{56}{9}[/tex] = -32

3x - [tex]\frac{224}{9}[/tex] = -32

3x = -32 + [tex]\frac{224}{9}[/tex]

3x = -[tex]\frac{288}{9}[/tex]+ [tex]\frac{224}{9}[/tex]

3x = -[tex]\frac{64}{9}[/tex]

x = -[tex]\frac{64}{27}[/tex] = -2

Answer:

The water costs $1.90, the chips are $.95 and the milk is $3.80.

Step-by-step explanation:

Let m = milk

Let w = water

Let c = chips

2m+6w+7c =25.65      w = 2c     m = w + 1.90

For the first equation, substitute w for 2C and m for w + 1.90 to get:

2(w+1.90) +6(2c) + 7c = 25.65

2w+3.8+12c+7c=25.65

2w+19c = 21.85

Now substitute 2c for w:

2(2c)+19c =21.85

4c + 19c = 21.85

23c = 21.85

c = .95  Now that we know the cost of the chips we can use that to find the water and the milk for the original equations that we wrote at the top.

w = 2c

w=2(.95) = 1.90

m = w + 1.90 = 1.90+1.90 = 3.80

Answer:  30 miles

Work Shown:

2 in : 6 mi

5*2 in : 5*6 mi

10 in : 30 mi

Answer:

-5

Step-by-step explanation:

The y coordinate of the vertex is -5.

Step-by-step explanation:

2y - x = 6

2y = x + 6

y = (x + 6) / 2

the slope is 1 and the y int is 3

Answer:

[tex] \pink{\maltese{ \text{BODMAS \:Full \: Form \: }}}[/tex]

The expression (48-24)÷3×4 as per BODMAS rule.

(48-24)÷3×4

=24÷3×4

=8×4

=32

Now,

The given question is,

Simplify:

[tex] \displaystyle{ \frac{7}{8} \div 5 \frac{1}{3} \times \frac{24}{7} }[/tex]

[tex] \displaystyle{ = \frac{7}{8} \div \frac{16}{3} \times \frac{24}{7} }[/tex]

[tex] \displaystyle{ = \frac{ \cancel{7} \times 3 \times \cancel{24} \: {}^{3} }{ \cancel{8 } \times 16 \times \cancel{7}} }[/tex]

[tex] \displaystyle{ = \frac{3 \times 3}{16} }[/tex]

[tex] \displaystyle{} = \frac{9}{16} [/tex]

Thus,the final answer is 9/16.

Solution -:

[tex] \frac{7}{8} \div 5 \frac{1}{3} \times \frac{24}{7} [/tex]

Let's begin-

solve,,,

Now,,According to BODMAS rule fist we divide ,

[tex] \frac{7}{8} \times \frac{3}{16} \times \frac{24}{7} \\[/tex]

Now , we multiple

[tex] \frac{3 \times 3}{16} \\ \\ = \frac{9}{16} [/tex]

and this is our final answers

▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃

Division → Multiplication → Addition → Subtraction

The type of reflection performed and the scale factor of dilation of the diagram are; Reflection over the x-axis and a scale factor dilation of 2.

From the given diagram, we are told that triangle ABC is transformed into Triangle A"B"C".

Now, we are told that both triangles are similar and as such if they are similar then, it means each corresponding side has the same ratio. Thus, there was a dilation by a scale factor of 2.

Now, the reflection that took place after the dilation would be a reflection over the x-axis.

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The graphed function is: y = (x + 2)(x − 1)(x − 3).

Option (a) is correct.

From the graph given in the question, it can be seen that the graph has 3 critical points, namely, x= -2, x = 1 and x = 3.

From all the five options given, the first option, that is, y = (x + 2)(x − 1)(x − 3), has the critical points x= -2, x = 1 and x = 3.

The critical points for a function are obtained by substituting the function to be equal to zero.

So, (x + 2)(x − 1)(x − 3) = 0

That is, x= -2, x = 1 and x = 3.

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The half-life of the given exponential function is of 346.57 years.

It is the value of t when A(t) = 0.5A(0).

In this problem, the equation is:

[tex]A(t) = A(0)e^{-0.002t}[/tex].

In which t is measured in years.

Hence the half-life is found as follows:

[tex]0.5A(0) = A(0)e^{-0.002t}[/tex]

[tex]e^{-0.002t} = 0.5[/tex]

[tex]\ln{e^{-0.002t}} = \ln{0.5}[/tex]

[tex]0.002t = -\ln{0.5}[/tex]

[tex]t = -\frac{\ln{0.5}}{0.002}[/tex]

t = 346.57 years.

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The number must be between 20 and 30.

The square of the whole number can be found as follows;

The square of the whole number is between 500 and 900. The number must be between 20 and 30.

The number is an whole number.

Therefore, the number will be between 20 and 30.

20² = 400

30² = 900

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The 53,000 units produced and the increase in sales of 50,400 - 48,000 = 2,400 units, give an impact (increase) in profit of $168,000

Price per unit = $70

Number of units produced = 53,000

Number of units sold = 48,000

Material cost per unit = $21

Labour cost per unit = $10

Manufacturing overhead = $2

Selling and administrative overhead = $4

Fixed cost = $1,060,000

Administrative expenses = $557,000

Advertising cost = $43,000

Percentage increase in sales = 20%

Number of units sold in Year 2 = 1.2 × 12,000 = 14,400

Total cost = 53000×(21+10+2+4) + 1,060,000 + 557,00 = 3,578,000

Total revenue in Year 1 = 70 × 48,000 = 3,360,000

Profit in Year 1 = 3,360,000 - 3,578,000 = -218,000

Total revenue in Year 2 = 70 × (36,000+14,400) = 3,528,000

Profit in Year 2 = 3,528,000 - 3,578,000 = -50,000

The impact on the profit is therefore;

-50,000 - (-218,000) = 168,000

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This problem is about pension fund management. It is to be noted that the best Feasible Capital Allocation Line (CAL) is: 0.3162.

A graph's capital allocation line depicts all conceivable combinations of risky and risk-free assets, allowing investors to estimate future returns depending on risk.

It is to be noted that the optimal risky portfolio's stock percentage is determined by:

Weight of Stock = ((Return on Stock - Risk Free Rate) * Variance of bond) - ((Return on Bond - Risk Free Rate) * Co-Variance of bond & Stock)/ ((Return on Stock - Risk Free Rate) * Variance of bond + (Return on Bond - Risk Free Rate) * Variance of Stock - ((Return on Bond - Risk Free Rate + Return on Stock - Risk Free Rate + ) * Co-Variance of bond & Stock)

→ The weight of stock

= ((15% - 5.5%) * 529) - ((9% - 5.5%) * 110.40)/ ((15% - 5.5%) * 529) + (9% - 5.5%) * 1,024 - ((15% - 5.5% + 9% - 5.5%) * 110.40)

= [(50.255) * (3.864) /(50.255) + (46.08) - (14.352)]

Weight of Stock = 0.646628

Weight of  Bonds = 1 - 0.646628

Weight of  Bonds= 0.353372

Expected return of portfolio = 0.646628 * 15% + 0.353372 * 9%

= 12.88%

Standard Deviation of Portfolio (SDP)= (0.6466282² * 1,024 + 0.3533722² * 529 + 2 * 0.646628* 0.353372* 110.40)⁰·⁵

SDP = (544.67)⁰·⁵

SDP = 23.34%

Hence,

Best feasible CAL = (12.88% - 5.5%)/ 23.34%

Best feasible CAL = 0.3162

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Full Question

See the attached spread sheet for additional information related to the questions.

Answer:

Step-by-step explanation: