Given that ƒ(x) = 3^x, identify the function g(x) shown in the figure. A) g(x) = −3^-x
B) g(x) = −(1∕3)^x
C) g(x) = 3^−x
D) g(x) = −3^x

Answer:

4 cm by 5 cm (4 x 5)

Step-by-step explanation:

The area of a rectangle with length [tex]l[/tex] and width [tex]w[/tex] is given by [tex]A=lw[/tex]. Since the length of the rectangle is 7 less than 3 times its width, we can write the length as [tex]3w-7[/tex]. Therefore, substitute [tex]l=3w-7[/tex] into [tex]A=lw[/tex]:

[tex]A=lw,\\20=(3w-7)w[/tex]

Distribute:

[tex]20=3w^2-7w[/tex]

Subtract 20 from both sides:

[tex]3w^2-7w-20=0[/tex]

Factor:

[tex](w-4)(3w+5)=0,\\\begin{cases}w-4=0, w=\boxed{4},\\3w+5=0, 3w=-5, w=\boxed{-\frac{5}{3}}\end{cases}[/tex]

Since [tex]w=-\frac{5}{3}[/tex] is extraneous (our dimensions cannot be negative), our answer is [tex]w=4[/tex]. Thus, the length must be [tex]20=4l, l=\frac{20}{4}=\boxed{5}[/tex] and the dimension of the rectangle are 4 cm by 5 cm (4 x 5).

Answer:

y = 3x^2-6x+3    one real solution  

y = -x^2 - 4x + 7     two real solution

y = -2x^2+9x-11       two complex solutions

Step-by-step explanation:

b^2-4ac = 0   1 repeated real solution

b^2-4ac > 0   2 distinct real solutions

b^2-4ac < 0   2 complex solutions

The quadratic functions have the following solutions:

y = 3x²-6x+3 has two real solutions.

y = -x² - 4x + 7 has one real solution.

y = -2x²+9x-11 has one complex solution.

The given quadratic functions are y = 3x²-6x+3, y = -x² - 4x + 7 and y = -2x²+9x-11.

The discriminant of a quadratic equation ax² + bx + c = 0 is in terms of its coefficients a, b, and c. i.e., Δ OR D = b² − 4ac.

Now, with the function y = 3x²-6x+3, we get

b² − 4ac=(-6)²-4×3×3=36-36=0

Since b=0 it has two real solutions.

Now, with the function y = -x² - 4x + 7, we get

b² − 4ac= (-4)²-4×(-1)×7=16+28=44

Since b>0 it has one real solutions.

Now, with the function y = -2x²+9x-11, we get

b² − 4ac= (9)²-4×(-2)×(-11)=81-88=-7

Since b<0 it has one complex solution.

Therefore, the quadratic functions have the following solutions:

y = 3x²-6x+3 has two real solutions.

y = -x² - 4x + 7 has one real solution.

y = -2x²+9x-11 has one complex solution.

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Answer:

Answer:

C 9i

D -9i

Step-by-step explanation:

sqrt(-81)

sqrt(81) sqrt(-1)

we know that sqrt(-1) = i

±9i

Answer:

68% of the time, John's grades will be between 55 and 85, while for Jane, 68% of the time, her grades will be between 65 and 75. They have the same mean grade, however, due to the lower standard deviation, Jane is more consistent, while John has the higher upside.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

John:

Mean of 70, standard deviation of 15.

70 - 15 = 55

70 + 15 = 85

68% of the time, John's grades will be between 55 and 85.

Jane:

Mean of 70, standard deviation of 5.

70 - 5 = 65

70 + 6 = 75.

68% of the time, Jane's grades will be between 65 and 75.

Describe the two students in terms of consistency of their grades and give reason.

68% of the time, John's grades will be between 55 and 85, while for Jane, 68% of the time, her grades will be between 65 and 75. They have the same mean grade, however, due to the lower standard deviation, Jane is more consistent, while John has the higher upside.

Answer:

1 = - 4 - 14 √3

2 = 9 - 11 √3

Step-by-step explanation:

Question 1

(-4√3 + 2)(√3 + 4)

Apply FOIL method

= (-4√3) √3 + (-4√3) . 4 + 2 √3 + 2 . 4

Apply minus-plus rules: + (-a) = -a

= -4 √3 √3 - 4 . 4 √3 + 2 √3 + 2 . 4

Simplify

= - 4 - 14 √3

Question 2

(-3 + √3)(1 + 4 √3)

Apply FOIL method

= (-3) . 1 + (-3) . 4 √3 + √3 . 1 + √3 . 4 √3

Apply minus-plus rules: + (-a) = -a

= -3 . 1 - 3 . 4 √3 + 1 . √3 + 4 √3 √3

Simplify

= 9 - 11 √3

Answer:

qualitative

Step-by-step explanation:

bcos the question is in quality format

Answer:

we are armysss!!!!\

hiiiiiiiiii

yoooooooo

heyyyyyy

brainlist meeee!

Answer:

m║n

Step-by-step explanation:

If two lines 'line m' and 'line n' are perpendicular to the 'line t', both the lines 'm' and 'n' will be parallel to each other.

If m ⊥ l and n ⊥ l, then m║n.

Answer:

4th option

Step-by-step explanation:

6/sin(65) = 5/sin(x)

or, 6×sin(x) = 5×sin(65)

or, sin(x) = 5×sin(65)/6

or, x = arcsin(5×sin(65)/6)

Answer:

4x + 3 = 59

x = 14

Step-by-step explanation:

The vertical angles theorem states that when two lines intersect, the angles opposite each other are congruent. One can apply this here by stating the following:

4x + 3 = 59

Solve for (x), use inverse oeprations:

4x + 3= 59

4x = 56

x = 14

Answer:

Relationship : Vertical angle

Step-by-step explanation:

(4x + 3) = 59

4x = 59 - 3

4x = 56

x = 56/4

x = 14

Answer:

[tex]P(O\ or\ A) = 0.85[/tex]

Step-by-step explanation:

Given

See attachment

Required

[tex]P(O\ or\ A)[/tex]

From the question, we understand that she can only get blood from O or A groups. So, the probability is represented as:

[tex]P(O\ or\ A)[/tex]

This is calculated as:

[tex]P(O\ or\ A) = P(O) + P(A)[/tex]

Using the American row i.e. the blood must come from an American.

We have:

[tex]P(O) = 0.45[/tex]

[tex]P(A) = 0.40[/tex]

So, we have:

[tex]P(O\ or\ A) = 0.45 + 0.40[/tex]

[tex]P(O\ or\ A) = 0.85[/tex]

Answer:

Number of planes on the runway or waiting to take off is approximately 2

Step-by-step explanation:

Given the data in the question;

On average there are 21 planes taking off per hour

rate of flow = frequency of take off = 21 planes / hr

= 21 planes per 60 minutes

= 0.35 planes/min

Now, we get the throughput time

throughput time = total time for take off =  waiting time on runway + run time on runway

= (4 minutes and 21 seconds) + 27 seconds

= 4.35 minutes + 0.45 minutes

= 4.8 minutes

Now, using Little's law;

Number of planes on the runway or waiting to take off will be;

N = Rate of flow × throughput time

we substitute

N = ( 0.35 planes/min ) × 4.8 min

N = 1.68 planes ≈ 2 planes

Therefore, Number of planes on the runway or waiting to take off is approximately 2

Answer:

1st row 56 pennies

2nd row 36 pennies

3rd row 14 dimes

4th row 4 quarters

5th row 5 nickels

Step-by-step explanation:

1st row $1.85 + 56 cents = $2.41

2nd row $2.05 + 36 cents = $2.41

3rd row is $1.01 + $1.40 = $2.41

4th row $1.41 + $1.00 = 2.41

5th row $2.16 + 25 cents = $2.41

Answer:

500000

Step-by-step explanation:

Answer:

[tex]m\angle H = 30^o[/tex]

Step-by-step explanation:

Given

See attachment

Required

Find [tex]m\angle H[/tex]

To calculate [tex]m\angle H[/tex], we make use of:

[tex]\cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]

So, we have:

[tex]\cos(H) = \frac{GH}{HI}[/tex]

This gives:

[tex]\cos(H) = \frac{10\sqrt3}{20}[/tex]

[tex]\cos(H) = \frac{\sqrt3}{2}[/tex]

Take arccos of both sides

[tex]m\angle H = cos^{-1}(\frac{\sqrt3}{2})[/tex]

[tex]m\angle H = 30^o[/tex]

Answer:

[tex]y=\frac{\displaystyle 3}{\displaystyle 50}x+\frac{\displaystyle 13}{\displaystyle 10}[/tex]

Step-by-step explanation:

Hi there!

Slope-intercept form: [tex]y=mx+b[/tex] where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept (the value of y when x is 0)

1) Determine the slope (m)

[tex]m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_1}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the given points (15,2.2) and (5,1.6):

[tex]m=\frac{\displaystyle 1.6-2.2}{\displaystyle 5-15}\\\\m=\frac{\displaystyle -0.6}{\displaystyle -10}\\\\m=\frac{\displaystyle 0.6}{\displaystyle 10}\\\\m=\frac{\displaystyle 0.3}{\displaystyle 5}\\\\m=\frac{\displaystyle 3}{\displaystyle 50}[/tex]

Therefore, the slope of the line is [tex]\frac{\displaystyle 3}{\displaystyle 50}[/tex]. Plug this into [tex]y=mx+b[/tex]:

[tex]y=\frac{\displaystyle 3}{\displaystyle 50}x+b[/tex]

2) Determine the y-intercept (b)

[tex]y=\frac{\displaystyle 3}{\displaystyle 50}x+b[/tex]

Plug in a given point and solve for b:

[tex]1.6=\frac{\displaystyle 3}{\displaystyle 50}(5)+b\\\\1.6=\frac{\displaystyle 3}{\displaystyle 10}+b\\\\1.6-\frac{\displaystyle 3}{\displaystyle 10}=\frac{\displaystyle 3}{\displaystyle 10}+b-\frac{\displaystyle 3}{\displaystyle 10}\\\\\frac{\displaystyle 13}{\displaystyle 10}=b[/tex]

Therefore, the y-intercept is [tex]\frac{\displaystyle 13}{\displaystyle 10}[/tex]. Plug this back into [tex]y=\frac{\displaystyle 3}{\displaystyle 50}x+b[/tex]:

[tex]y=\frac{\displaystyle 3}{\displaystyle 50}x+\frac{\displaystyle 13}{\displaystyle 10}[/tex]

I hope this helps!

Answer:

y - 8 = -2(x + 1)^2

Step-by-step explanation:

The vertex of this parabola is (-1, 8).  It opens downward, so the x^2 term has a negative coefficient.  The zeros are (-3, 0) and (1, 0), and the y-intercept is (0, 7).

Through the vertex form of the equation of a parabola we get:

y - (8) = a(x - (-1)) + 7, or

y - 8 = a(x + 1)^2.  Find coefficient a by substituting the coordinates (-3, 0) in this equation:

0 - 8 = a(-3 + 1)^2, or

-8 = a(-2)^2, or a = -2

The desired equation is

y - 8 = -2(x + 1)^2

Answer:

Answer is -1

Step-by-step explanation:

i1 = i 

i2 = -1 

i3 = -i

i4 = 1

i0 × i1 × i2 × i3 × i4 = 1 × i  × (- 1) × (- i) × 1 = i2 = - 1

Answer:the answer is -1

Step-by-step explanation:

Step-by-step explanation:

The relation between kg and lbs is :

1 kg = 2.2046 lbs

We need to find the values of 1kg/2.2046lbs and 2.2046lbs/1kg.

So,

[tex]\dfrac{1\ kg}{2.2046\ lbs}=\dfrac{2.2046\ lbs}{2.2046\ lbs}\\\\=1[/tex]

and

[tex]\dfrac{2.2046\ lbs}{1\ kg}=\dfrac{2.2046\ lbs}{2.2046\ lbs}\\\\=1[/tex]

Hence, this is the required solution.

Answer:

Both are same as 1.

Step-by-step explanation:

1 kg = 2.2046 lbs

So,

[tex]\frac{1 kg}{2.2046 lbs }=\frac{1 kg }{1 kg} = 1[/tex]

And

[tex]\frac{2.2046 lbs}{1 kg }=\frac{1 kg }{1 kg} = 1[/tex]

Answer:

closing price of the fast food stock was $997.50

closing price of the toy company stock was $598.50

the price per fast food share was $28.50

Step-by-step explanation:

x = price per share fast food

y = price per share toy company

35x + 63y = 1596

x = y + 19

=>

35(y+19) + 63y = 1596

35y + 665 + 63y = 1596

98y + 665 = 1596

98y = 931

y = $9.50

=>

x = 9.5 + 19 = $28.50

the value of the whole fast food stock was

35x = 35×28.5 = $997.50

the cake if the whole toy company stock was

63y = 63×9.5 = $598.50

Answer:

The man would be 40 years old.

Step-by-step explanation:

Blood pressure as function of age:

Is given by the following equation:

[tex]P = 0.006A^2 - 0.02A + 120[/tex]

Find the age of a man whose normal blood pressure measures 129 mmHg.

This is A for which P = 129. So

[tex]129 = 0.006A^2 - 0.02A + 120[/tex]

[tex]0.006A^2 - 0.02A - 9 = 0[/tex]

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]

[tex]\Delta = b^{2} - 4ac[/tex]

In this question:

Quadratic equation with [tex]a = 0.006, b = -0.02, C = -9[/tex]. So

[tex]\Delta = (-0.02)^2 - 4(0.006)(-9) = 0.2164[/tex]

[tex]A_{1} = \frac{-(-0.02) + \sqrt{0.2164}}{2*(0.006)} = 40.4[/tex]

[tex]A_{2} = \frac{-(-0.02) - \sqrt{0.2164}}{2*(0.006)} = -37.1[/tex]

Age has to be a positive number, so rounding to the nearest year:

The man would be 40 years old.

Answer:

Small (11.5) is 37 cents per ounce.

Large (27.8) is 36 cents per ounce.

27.8 ounces is the better buy.

=================================================

Work Shown:

ED/DF = AB/AC

x/24 = 12/16

16x = 24*12

16x = 288

x = 288/16

x = 18

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

Explanation:

Because the triangles are similar, we can form the proportion shown above. There are many variations of the proportion that can happen, but they all lead to the same result x = 18.

So for instance, another proportion you could solve is ED/AB = DF/AC.

The key is to keep up the same pattern when forming the ratios.

What I mean by that is when I formed ED/DF I divided the vertical side over the horizontal side for triangle EDF. So to form the second fraction, we must do the same division (vertical over horizontal) for triangle ABC.

Answer:

It multiplies

Step-by-step explanation:

if the number of hours changes to example to 2 then you multiply 60 by 2 resulting in 120miles in 2 hours

Answer:

skewness

Step-by-step explanation:

Average.

The average of a set of observations is the most important and useful measure of statistics and is a position measure, as it shows the positions of the numbers to which it refers. The average value is involved in several types of statistics and is examined in almost all statistical distributions. It is generally defined as the sum of the observations by their number. That is, it is the mathematical operation of finding the "mean distance" between two or more numbers.

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Answer:

2/12 = 1/6

Step-by-step explanation:

To find the probability of something with an equal chance of each outcome, we can apply the formula (number of favorable outcomes)/(number of total outcomes). Because there is an equal chance for each side of the die to be landed on, we can apply this.

On a 12 sided die, there are 12 sides. Two of those sides are 3 and 9. Therefore, there are two favorable outcomes (3 and 9). There are 12 sides to choose from, so there are 12 total outcomes, making the probability 2/12 = 1/6

Answer:

[tex]\boxed{\sf A) ( 1,0) }[/tex]

Step-by-step explanation:

A quadratic function is given to us and we need to find the x Intercept of the graph of the given function . The function is ,

[tex]\sf \implies f(x) = x^2 -2x + 1 [/tex]

For finding the x intercept , equate the given function with 0, we have ;

[tex]\sf \implies x^2 -2x + 1 = 0 [/tex]

Split the middle term ,

[tex]\sf \implies x^2-x-x+1=0[/tex]

Take out common terms ,

[tex]\sf \implies x( x -1) -1( x -1) = 0[/tex]

Take out (x - 1 )as common ,

[tex]\sf \implies (x - 1 )(x-1) = 0[/tex]

Equate with 0 ,

[tex]\sf \implies x = 1,1 [/tex]

Therefore the root of the function is 1. Hence the x Intercept is (1,0)

Hence the x Intercept is (1,0) .

Step-by-step explanation:

x² - 2x + 1 = 0

x² - (x + x) + 1 = 0

x² - x - x + 1 = 0

x(x - 1) - 1(x - 1) = 0

(x - 1)(x - 1) = 0

x = 1

Hence,

Option A

Answer: p >-17/5

Step-by-step explanation:

Answer:

P = [tex]\frac{-17}{5}[/tex]

Step-by-step explanation:

Substract 3P from both sides:

5P  + 2 >  - 15

Subtract 2 from both sides:

5P > -17

Divide both sides by 5:

P = [tex]\frac{-17}{5}[/tex]