True or false: the variable in an exponential function is always the exponent of the power.

Answer:

a) m = -6/5

b) m = -5/6

Step-by-step explanation:

The slopes of parallel lines are the same. The parallel line will have a slope equal to that of the line it is parallel to, -6/5.

__

The slopes of perpendicular lines are the opposite of the reciprocal of one another. The perpendicular line will have a slope that is the negative reciprocal of the slope of the one it is perpendicular to: -1/m = -1/(6/5) = -5/6.

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In Algebra, angles are measured counterclockwise (CCW), generally using the +x axis as a reference. Thus any angle with an arrow shown in the CW direction will have a negative measure.

Know that clockwise measured angles are negative and anticlockwise measured angles are positive in sign.

Thus,

It is a standard convention used in mathematics that if you measure an angle clockwise(like the clock's hand moves), then the measured angle will be written with negative sign.

If the angle is measured anticlockwise, then the measured angle is written with positive sign.

Thus, by these conclusions, we have:

Learn more about sign of angles here:

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The domain and range is all real numbers.

Answer:

D) Domain: (-∞, ∞)

Range: (-∞, ∞)

Step-by-step explanation:

The domain is the input values, or the x values.

We can put in any x values for this function.

Domain : (-∞, ∞)

The range is the output values or the y values.

We can get any output values for this function

Range: (-∞, ∞)

Answer:

4

Step-by-step explanation:

You may recognize these as factors of the difference of two squares:

... a² -b² = (a+b)(a-b)

where a=1 and b=i√3.

Then the product is ...

... 1² -(i√3)² = 1 - 3i² = 1 +3 = 4

_____

Of course, i = √-1, so i² = -1.

Answer: 4

Step-by-step explanation:

u=(1+i√3) =2       v=(1-i√3)=2        Uv = (2)(2)=4

Answer:

2, 120 degrees

Step-by-step explanation:

The first step in finding the polar form is finding the modulus, r

r= sqrt( x^2 + y^2)

r = sqrt( (-1)^2 + sqrt(3)^2)

r = sqrt(1+3)

r= sqrt(4)

r =2

The next step is finding the angle

theta = arctan (y/x)

theta = arctan (sqrt(3)/-1))

theta = arctan (-sqrt(3))

theta = -60

The point (-1, sqrt(3)) is in the 2nd quadrant, but our angle is in the 4th quadrant, so we add 180 degrees

theta = -60 + 180 = 120

theta = 120 degrees

Answer:

22,332

Step-by-step explanation:

Put 6 where t is in the equation and do the arithmetic.

... y = 5500 ln(9·6 +4) = 5500 ln(58) ≈ 22,332

Answer:

The answer is: 22,332 mowers will be sold 6 years after a model is introduced.

Step-by-step explanation:

Given that y = 5500 ln (9t + 4)

In order to calculate the number of mowers (y) that will be sold after 6 years, substitute t = 6 (years):

y = 5500 ln (9 × 6 + 4) = 5500 In 58

In 58 = natural logarithm of 58 = 4.0604

Therefore, y = 5500 In 58 = 5500 × 4.0604 = 22,332.44 = 22,332 mowers.

Answer:

Hence, Option 1 is correct equation [tex]s=4\sqrt{d}[/tex]

Step-by-step explanation:

The distance it takes a car to come to a complete stop after the brakes are applied is related to the speed that the car is traveling. the stopping distances and speeds are shown in the table.

     d         s  

    20      17.89

    40      25.30

    60      30.98

    80      35.78

  100       40.00

We will check each option for table.

[tex]s=4\sqrt{d}[/tex]

For d=20, Put d=20 into [tex]s=4\sqrt{d}[/tex]

[tex]s=4\sqrt{20}\approx 17.89[/tex]

For d=40, Put d=40 into [tex]s=4\sqrt{d}[/tex]

[tex]s=4\sqrt{40}\approx 25.30[/tex]

For d=60, Put d=60 into [tex]s=4\sqrt{d}[/tex]

[tex]s=4\sqrt{60}\approx 30.98[/tex]

For d=80, Put d=80 into [tex]s=4\sqrt{d}[/tex]

[tex]s=4\sqrt{80}\approx 35.78[/tex]

For d=100, Put d=100 into [tex]s=4\sqrt{d}[/tex]

[tex]s=4\sqrt{100}\approx 40.00[/tex]

All the value of table satisfy the first equation.

Hence, Option 1 is correct equation [tex]s=4\sqrt{d}[/tex]

Answer:

x = 3   and x=-6/5

Step-by-step explanation:

x = one integer

y = other integer

One integer is 9 less than 5 times another

x= 5y-9

product is 18

xy = 18

Substitute in for x

(5y-9) *y = 18

Distribute

5y*y -9y = 18

5y^2 - 9y = 18

Subtract 18 from each side.

5y^2 - 9y -18= 18-18

5y^2 - 9y -18 = 0

Using the quadratic formula

-b ± sqrt(b^2 -4ac)

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

2a

-(-9) ±sqrt(9^2 -4*5*(-18))

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

2(5)

9 ±sqrt(81 +360))

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

10

9 ±sqrt(441)

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

10

9±21

----------

10

x = (9+21)/10   and x = (9-21)/10

x = 30/10   and x = (-12)/10

x = 3   and x=-6/5

Final answer:

The two integers in question are 21 and 6, with 21 being 9 less than 5 times 6, and their product equating to 18.

Explanation:

Finding the Two Integers

The problem states that one integer is 9 less than 5 times another integer, and their product is 18. Let's call the first integer x and the second integer y.

From the problem, we can write two equations:

x = 5y - 9 (One integer is 9 less than 5 times the other)

xy = 18 (The product of the two integers is 18)

Using substitution from the first equation, in the second equation, we replace x with 5y - 9 and solve for y:

(5y - 9)y = 18

This equation leads to a quadratic equation: 5y^2 - 9y - 18 = 0. Factoring the quadratic equation, we find two pairs of numbers that multiply to give -18 and add up to -9: (-6) and 3.

The factors of the equation are (5y + 3)(y - 6) = 0, giving us y = 6 or y = -³/₅. However, since we are looking for integers, we disregard the fraction and only consider y = 6. Plugging y = 6 back into x = 5y - 9, we get x = 5(6) - 9 which simplifies to x = 21.

Therefore, the two integers are 21 and 6.

Answer:

hello :

- 3π/4  = (-3×180°)/4 =  - 540°/4 = - 135°

Step-by-step explanation:

Answer: [tex]\bold{-\dfrac{3}{4}\pi}[/tex]

Step-by-step explanation:

Set up a proportion using π = 180°  →   [tex]\dfrac{\pi}{180} = \dfrac{x}{-135}[/tex]

Multiply both sides by -135 to solve for x  →  [tex]\dfrac{-135\pi}{180} = x[/tex]

Simply the fraction by dividing by [tex]\dfrac{45}{45}[/tex] →  [tex]-\dfrac{3}{4}\pi = x[/tex]

Answer:

87600

Step-by-step explanation:

Answer:

87600 hours

Step-by-step explanation:

1 decade = 10 years

1 year = 365  days

1 day = 24 hours

1 decade * 10 years/ 1 decade  * 365 days/ 1 year  * 24 hours / 1 day

87600 hours

Answer:

4 people

Step-by-step explanation:

You Know that 1/3 of an hour is 20 min, and u find out that 1/4 of an hour is 15 min. So then it takes 45 min for 1 person. 3 1/3 hour= 3 hr 20 min= 200 min. 200/45=4.44...= 4 people

Assume x is a whole number. Then 2x+1 is a whole number, and 7(2x+1) is a whole number that is a multiple of 7.

13 is not a multiple of 7, so we have reached a contradiction, and our assumption must be false.

x cannot be a whole number.

You can go at this in different ways. In the attached, we multiplied the number of pounds by the sale price per pound ($5.25/4.2). You can also figure the price per pound of each proposed purchase and compare with the sale price.

... sale price = $5.25/(4.2 lb) = $1.25/lb

(A) $7.60/(6 lb) = $1.25/lb (yes)

(B) $4.25/(3.4 lb) = $1.25/lb (yes)

(C) $4.20/(3.5 lb) = $1.20/lb (no)

(D) $8.70/(5.8 lb) = $1.50/lb (no)

(E) $2.50/(2 lb) = $1.25/lb (yes)

Options A (6 pounds for $7.50), B (3.4 pounds for $4.25), and E (2 pounds for $2.50) are proportional to the sale price as their unit prices match, whereas options C (3.5 pounds for $4.20) and D (5.8 pounds for $8.70) do not match the unit price and are thus not proportional.

To determine if the proportions are equivalent to the sale price of green beans, we need to calculate the unit price for each scenario and compare it to the unit price that Mrs. Reynolds paid during the sale. Mrs. Reynolds bought 4.2 pounds of green beans for $5.25. The unit price is found by dividing the total cost by the total weight in pounds:

Unit price = $5.25 / 4.2 pounds = $1.25 per pound.

Now, let's calculate the unit price for each of the given scenarios and see if they match the unit price Mrs. Reynolds paid:

Based on these calculations, options A, B, and E are proportional to the sale price Mrs. Reynolds paid, while options C and D are not.

Answer:

B: The mean study time of students in Class B is less than students in Class A.

Step-by-step explanation:

To find out why answer B is the right answer, I will give you facts from each option.

Option A is false. The mean study time in Class A is 4.8. Meanwhile in Class B it is 4. For Class A, sum up the 20 study times which is 96 and divide them by 20, you will get 4.8 hours of mean study time. For Class B, the sum of the 20 study times is 80, which divided by 20 will be 4.

Option B is True. See previous explanation.

Option C is False. The median study time in Class B is 4. The median study time in Class A is 4.8,

Option D is False. The range in Class A is from 2 to 8. The range in Class B is from 2 to 7.

Option E is False: The mean and median study time of these classes is different.

Answer:

B: The mean study time of students in Class B is less than students in Class A.

Step-by-step explanation:

If Alex cut his wire 18 times, he ended up with 19 equal pieces. He kept 7, so has 7/19 of his 1/3 of the wire.

Bob cut his wire 20 times, so ended up with 21 pieces, of which he kept 9. So he has 9/21 = 3/7 of his 1/3 of the wire.

Claudia kept 1/13 of her 1/3 of the wire, so has the smallest piece.

Bob kept (3/7)·(1/3)·126 cm = 18 cm.

Alex kept (7/19)·(1/3)·126 cm ≈ 15.47 cm.

Bob kept the longest part of the original wire.

Final answer:

The median is found by arranging a data set in ascending order and locating the middle value for an odd number of values or averaging the two middle values for an even number. Quartiles divide the data into sections and are related to the median. The median offers a measure of the center that is not skewed by outliers.

Explanation:

To find the median of a data set, start by arranging the data in ascending order. If the data set has an odd number of values, the median is the middle value. If the data set has an even number of values, calculate the median by taking the average of the two middle values.

For example, for the ordered data set 3, 4, 8, 8, ... 44, 44, 47, which has 40 values, the median is between the 20th value (24) and the 21st value (24). In this case, since they are the same number, the median is 24. However, if the two numbers were different, you would add them together and divide by two to find the median.

When considering a data set like 1, 1, 2, 2, 4, 6, 6.8, 7.2, 8, 8.3, 9, 10, 10, 11.5, with an even number of values (14), the median is the average of the 7th and 8th values, in this case, (6.8+7.2)/2 = 7. The quartiles can also be determined: Q1 is the median of the lower half, and Q3 is the median of the upper half of the data set.

Measures of the center of the data, like mean, median, and mode, offer different ways to represent the data set's central tendency. The median is particularly useful in data sets with outliers, as it is not as affected by extreme values as the mean.

Answer:

x ∈ {-2, 1, 4}

Step-by-step explanation:

The graph shows y = 0 when x = -2 or 1 or 4. Hence these values of x are the zeros of the function.

Answer:

Value of the car is decreasing by 13.9% each year.

Step-by-step explanation:

This equation tells us V(t) is the value of the car after a certain time in years, $21,000 is the initial value of the car.  What we need to focus on is on the 0.861 part of this equation.  This means that the price of the car is worth 0.861 or 86.1% of what it was worth the year prior, this means that the price of the car is decreasing over time.  By how much is it decreasing? Well if we consider 1 to mean 100% (since 100 / 100 =1) then we have 100%-86.1%=13.9%.  This means that the value of the car is decreasing 13.9% each year.

Answer:

34.32%

Step-by-step explanation:

Tom is 45 years old.

Tom earning = $5950 per month

Mortgage payment = $2042

Percentage of amount paid towards mortgage in his income = (2042/5950)*100

=  34.32%

Tom pays 34.32% of his income towards mortgage.

The national average of his age group pays 35% of income towards housing.

Thank you.

Given zeros -4, -3, and 1, and a y-intercept of -11, the corresponding third-degree polynomial function can be formulated as y = (11/12)(x + 4)(x + 3)(x - 1).

To construct a third-degree polynomial function, we first need to define the polynomial based on its zeros. Given that the zeros are -4, -3, and 1, we can write the polynomial function in the form [y = a(x + 4)(x + 3)(x - 1)], where 'a' is the coefficient that affects the y-intercept. Because the y-intercept is -11, we set the value of y to -11 when x equals 0 to solve for 'a'. Thus the equation becomes [ -11 = a * 4 * 3 * -1], which simplifies to [a = -11/(-12) = 11/12]. Therefore, the polynomial function with the stated properties is [y = (11/12)(x + 4)(x + 3)(x - 1)] .

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The third-degree polynomial with zeros at -4, -3, and 1 and a y-intercept of -11 can be written as P(x) = 0.917(x+4)(x+3)(x-1).

To construct a third-degree polynomial with zeros at -4, -3, and 1, we write the factored form of a polynomial P(x), with the zeros plugged into the factors: P(x) = a(x+4)(x+3)(x-1). The term 'a' is a coefficient that we can find using the provided y-intercept of -11.

Because the y-intercept happens when x = 0, we substitute x = 0 and y = -11 into the polynomial: -11 =a(0+4)(0+3)(0-1). Solving for 'a' gives a = 11/12 or 0.917.

Thus, the resulting third-degree polynomial in lowest terms is P(x) = 0.917(x+4)(x+3)(x-1).

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Answer:C

Step-by-step explanation:

Formula must be S(x) = (1+1/2)√x = 1.5√x, eliminating A and D. Diagram must show that a zero length boat doesn't move, and that boat length four feet goes 1.5×2 = 3 knots. That eliminates B. Check: C says zero feet goes zero knows and 4 feet goes 3 knots.

Answer:

Graph C

Step-by-step explanation:

We know the speed is equal to one and a half times the square root of the length.  This means that speed is the dependent variable (y), and length is the independent variable (x).  

Since the speed, S(x), is 1.5 times the square root of the length (x), we get the function

S(x) = 1.5√x.

When x = 0, S(x) = 1.5√0 = 1.5(0) = 0.  This makes it graph C.

Answer:

x=6       x=4

Step-by-step explanation:

x^2 - 10x + 24 =0

We need to factor this equation

What numbers multiply together to give us 24 and add together to give us -10

-6* -4 = 24 and -6+-4 = -10

(x-6) (x-4) = 0

Using the zero product property

x-6 = 0   x-4=0

x=6       x=4

Answer:

1.)C

2.)A

3.)B

Step-by-step explanation:

edge 2024

Answer:

The length of a 180° arc of a unit circle is π ≈ 3.14 units.

Step-by-step explanation:

Use your knowledge of the circumference of a circle (the length full around) and the fact that there are 360° in the central angle of a full circle. The distance around is proportional to the angle, so an arc of measure 180° will have a length equal to

... (180°/360°) × circumference = (1/2)×circumference

For a unit circle, the circumference is 2π (= π×diameter = 2π×radius). Half that length is π units.

Answer:

A central angle of 180 degrees corresponds to half of the unit circle, and the circumference of the unit circle is 2π units. So, the distance traveled along the unit circle from the point (1, 0) is half of the circumference, which is 1/2 * 2π = π units. Thus, the answer is 3.14 units (approximately).

Answer:

B

Step-by-step explanation:

8x + 8y = 24

-8x on both sides

8y = -8x + 24

Divide by 8 on both

y = -x + 3

Answer:

B

Step-by-step explanation:

(÷8)8x + 8y = 24(÷8)

x + y = 3

y = - x + 3

If x is negative, then the function is decreasing.

y = - x + 3

When x = 0

y = - 0 + 3

y = 3

(0,3)

When y = 0

- x + 3 = 0

- x = - 3

x = 3

(3,0)

Alternative B

I hope I helped you.

Answer:

D) [tex](x-5)^2 + (y-2)^2 = 49[/tex]

Step-by-step explanation:

Center is (5,2) and radius = 7

We use center - radius form of equation of circle

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

Where (h,k) represents the center

and r is the radius of the circle

We know center is (5,2)  so h= 5  and k =2

r= 7

Plug in all the values

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

[tex](x-5)^2 + (y-2)^2 = 7^2[/tex]

[tex](x-5)^2 + (y-2)^2 = 49[/tex]

5 book covers and 2 boxes of pencils

If all 7 were book covers, the cost would be 10.50. The cost is 2.60 more than that. Each box of mechanical pencils costs 1.30 more than a book cover, so there must be 2.60/1.30 = 2 boxes of mechanical pencils (and 5 book covers).

_____

If you want an equation, let p represent the number of pencil boxes. Then 7-p is the number of book covers.

... 1.50(7-p) +2.80p = 13.10

... 1.30p = 13.10 -10.50 . . . . . subtract 10.50, collect terms

... p = 2.60/1.30 = 2 . . . . pencil boxes

... 7-2 = 5 . . . . . book covers

Answer:

Domain: (-infinity, infinity)    Range:  (-infinity, infinity)

Step-by-step explanation:

They are parabolas, therefore you can assume that they go on infinitely. To find range, you must look at your y values. Look for your lowest point. Because the line goes done forever, your beginning mark would be (-infinity.

To find the other part, you look at your positive y values. Look for the highest value. Because this goes on infinitely, the completed version of your notation would be (-infinity, infinity). Be sure to use the infinity symbol though, which looks like an 8 rotated 90 degrees.

To find domain, look at your x values. To begin, look at your left-most values, which would be the negative numbers. Because the line goes on forever to the left, your notation would be (-infinity. To find the other part of domain, look at your positive x values. Because this line goes on infinitely as well, the completed version of your notation would be (-infinity, infinity). Infinity is never bracketed, it is always in parenthesis.

Answer:

y= 5x-3

Step-by-step explanation:

We have an intercept of -3 and a slope of 5

We can use the slope intercept form of the equation

y= mx+b where m is the slope and b is the y intercept

Substituting in the known values.

y= 5x-3

Answer:

y = .025x +20

The y intercept is the value when x = o, or the starting value.  In this case, it is the temperature in degrees F at a depth of 0 meters.

Step-by-step explanation:

We have a point a (0,20) and a point at (2 , 20.05)

We can find the slope from

m = (y2-y1)/(x2-x1)

   = (20.05-20)/(2-0)

   = .05/2

     =.025

One of the points (0,20) is the y intercept  since x=0

We can use the slope intercept form of the equation

y= mx+b

y = .025x +20

The y intercept is the value when x = o, or the starting value.  In this case, it is the temperature in degrees F at a depth of 0 meters.

Answer:

.

Step-by-step explanation:

Answer:

The answer is 560

Step-by-step explanation:

multiply 420 by .75 for 75%

(420).75=560