For which of these functions does the function value change at a constant rate per unit change in x? Explain.

Answer:

∠DBC = 40°

Step-by-step explanation:

∠5 = ∠3 + ∠4 = 180° - ∠6 . . . . relationship of angles at a transversal, vertical angles

∠3 = 180° - ∠1 - ∠2 . . . . . . sum of angles of a triangle

Then

∠4 = 180° - ∠6 - (180° - ∠1 - ∠2) = ∠1 +∠2 -∠6 . . . . substitute for ∠3

∠4 = 65° +60° -85° = 40°

∠4 = ∠DBC = 40°

Answer:

y = 3x +8

Step-by-step explanation:

The slope of the given line is -1/3. The slope of a perpendicular line is the opposite of the reciprocal of that: -1/(-1/3) = 3.

Then, in point-slope form, the equation of the line is ...

... y - k = m(x - h) . . . . . for slope m through point (h, k)

... y - 5 = 3(x -(-1)) . . . . . for line of slope 3 through (-1, 5)

... y = 3x +8 . . . . . . . . . simplify

Answer:

2/(7a) < x < 7

Step-by-step explanation:

The product of roots of ax² +bx +c is c/a. In this case, that means the second root of the equation is ...

... 2/(7a)

Since a < 0, the parabola opens downward and 2/(7a) < 0. The quadratic function will be positive between the two roots, on the interval ...

... 2/(7a) < x < 7

Answer:

Without an actual drawing to show which side is 74 inches, then the answer could either be the square root of 6052 inches OR 70 inches.  

Step-by-step explanation:

All right triangles follow the rule of the pythagorean theorem, which states that a^2 + b^2 = c^2, where 'a' and 'b' represent the legs of a triangle and 'c' represents the hypotenuse.  The legs of a right triangle are the two sides that come together to form the 90 degree angle and the hypotenuse is the angled line across from the 90 degree angle.  In this case, the height would have to represent one of the legs, while the other 'side' would need to represent either a leg or the hypotenuse (depending on the actual diagram presented which is not shown in the problem posted).  So, if you substitute the values given into our legs, or 'a' and 'b', you would end up with the value of 'c' as the square root of 6052.  However, if the given side is actually the hypotenuse, you would solve by subtracting the c^2 from a^2 to get 'b'=70 inches.  

The height of the right angle triangle is 70 inches

Using Pythagoras's theorem for right angle triangle

c²  = a² + b²

where

c = hypotenuse

a and b are the other 2 legs.

Therefore,

c = 74 inches

a = 24 inches

74² = 24² + b²

5476  = 576 + b²

5476 - 576 = b²

b² = 4900

square root both sides

b = √4900

b = 70 inches

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Answer:

D) 15

Step-by-step explanation:

We know the formula for direct variation is  

y=kx

Substituting y=5 and x=4 we can calculate k

5=k4

Divide each side by 4

5/4 =k

Now y= 5/4 x

If x =12

y =5/4*12

y = 15

Answer:

1920 cm^3

Step-by-step explanation:

Divide into the rectangular prism on top, and the one on the bottom. Whole = sum of parts, so you find the volumes of those two separately and add them together to get the total.

V of rectangular prism = l x w x h (length x width x height)

Top:

l = 10

w = 8

h = 14 - 10 = 4

10 x 8 x 4 = 320

Bottom:

l = 10 + 10 = 20

w = 8

h = 10

20 x 8 x 10 = 1600

1600 + 320 = 1920

The volume of the rectangular prism together with subparts is 1920 cubic meters.

The volume of the rectangular prism is the product of the length, breadth, and height of the given prism.

Volume of rectangular prism = (length x width x height)

Divide into the rectangular prism on top, and the one on the bottom.

total volume = sum of parts, so we need to find the volumes of those two separately and add them together to get the total.

Top

l = 10

w = 8

h = 14 - 10 = 4

The volume of the rectangular prism = length x width x height

= 10 x 8 x 4 = 320

Bottom

l = 10 + 10 = 20

w = 8

h = 10

The volume of the rectangular prism = length x width x height

= 20 x 8 x 10 = 1600

The total volume of the shape = 1600 + 320 = 1920

Learn more about volume;

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Answer:

the first selection (see below)

Step-by-step explanation:

The average rate of change (m) on the interval [x1, x2] is given by ...

... m = (g(x2) -g(x1))/(x2 -x1)

For g(x) = -x²-4x and (x1, x2) = (6, 8), the expression is the one attached.

Answer:

[tex]\frac{[-8^2 - 4(8)]- [-6^2 - 4(6)]}{8-6}[/tex]

Step-by-step explanation:

average rate of change of the function g(x) = -x^2 - 4x on the interval 6 ≤ x ≤ 8

To find average rate of change we use formula

Average =[tex]\frac{g(x_2)-g(x_1)}{x^2-x_1}[/tex]

use the given interval 6<=-x<=8

x2=8  and x1= 6

we replace the value in the given formula

g(x) = -x^2 - 4x

[tex]g(8) = -8^2 - 4(8)[/tex]

[tex]g(6) = -6^2 - 4(6)[/tex]

x2-x1 is 8-6

So equation becomes

[tex]\frac{[-8^2 - 4(8)]- [-6^2 - 4(6)]}{8-6}[/tex]

First differences start at 1 and increase by 2.

Whenever analyzing any sort of sequence, it is usually helpful to look at the differences between terms. Here, they are ...

... 1, 3, 5, 7

This set of numbers clearly increases by 2 from one to the next. That is, second differences are 2.

_____

When 2nd differences are constant, the pattern can be described by a 2nd-degree polynomial. In this case, that is

... n² -2n +2 . . . . for n = 1, 2, 3, ...

Answer:

Quadratic sequence with

nth term = n^2 - 2n + 2.

Step-by-step explanation:

1,2,5,10,17

The differences between terms  are

1,3,5,7

and the second differences are

2,2,2

This is a quadratic sequence  with first term n^2  ( where n = sequence number).

List the original sequence and the values of n^2:-

1  2  5  10  17

1  4  9  16  25

If we subtract the first list from the second we get

0  2  4  6  8   which is arithmetic with common difference  2 and first term 0

The nth term of this is 2(n - 1)

So the explicit formula for the nth term of the original sequence is

n^2 - 2(n - 1)

= n^2 - 2n + 2

See the attachment

In this context, "x" stands for "a number". Then 1/2x is "one-half of a number" and 3/4x is "three-fourths of a number."

3/4 - ( ) means "three-fourths minus ..."

( ) + 1/2 means "one-half more than ..." or "the sum of ... and one-half."

Putting these ideas together lets you choose the phrases as indicated below.

14.4

This is a special case of the situation where two secant lines intersect a circle. The product of the near distance to the circle and the far distance to the circle from their point of intersection is a constant. A tangent is a degenerate case, where the near and far intersection points with the circle are the same point.

So, ...

... x · x = 9 · (9+14)

... x = 3√23 ≈ 14.4 . . . . . taking the square root

_____

Additional note on the geometry

This rule for the product of segments of secant lines also applies when the secants intersect inside the circle.

Answer:

14.39

Step-by-step explanation:

Theorem 12-15 III

(y+z) y=t squared

(9+14)9=x squared

23•9=x squared

207 =x squared

Square root of 207 is 14.39

1 minute = 60 seconds.

Multiply the speed per second by 60 to get speed per minute:

8 * 60 = 480 miles per minute.

Multiply speed per minute by number of minutes to get total miles traveled:

480 * 6 = 2,880 total miles.

Answer:

14 years 7 months

Step-by-step explanation:

If the average age was increased by 2 months by adding a 7th child, the total age was increased by 2·7 months = 14 months more than the previous average. That is, the added child's age is 14 months more than the previous average, so is ...

... (13 years + 5 months) + (1 year + 2 months) = 14 years + 7 months

_____

For the non-believers:

The previous total of all ages was ...

... 6 × (13 years 5 months) = 80 years 6 months

The new total of all ages is ...

... 7 × (13 years 7 months) = 95 years 1 month

The amount added to the previous total is ...

... (95 1/12 - 80 6/12) years = 14 7/12 years = 14 years 7 months

To find the age of the seventh child, calculate the total age of the six children and the total age of all seven children.

To solve this problem, we can use the concept of the average. Step 1: Calculate the total age of the six children by multiplying the average age (13 years and 5 months) by the number of children (6). Step 2: Calculate the total age of all seven children by multiplying the new average age (13 years and 7 months) by the total number of children (7). Step 3: Subtract the total age of the six children from the total age of all seven children to find the age of the seventh child.

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You want to determine the number of text messages students at your school send in a month. You randomly ask 10 students from each grade.

This is a random sampling method.

This sampling method is a basic sampling method where we select a group of subjects (a sample) for study from a larger group or  population. Each individual is chosen entirely by chance. Each member of the population has an equal chance of being included in the sample.

Answer:

answer is pretty much in the last sentance lol. random

Step-by-step explanation:

See attached graphs.

You are being asked to observe the graphs of the various equations and identify something they have in common. To answer the question, it usually works well to do exactly what the question asks you to do.

a: All three lines have a slope of at least 1 and pass through the origin.

b: These lines all have the same slope. They are parallel.

c: All three lines have a slope less than 1 and pass through the origin.

d: These are all the same line.

e: All of these lines intersect at the point (2, -2).

_____

Comment on the graphs

The number of attachments allowed here is limited, so some graphs have been combined. Where there are 3 lines, the first is red, the second is blue, the third is green.

Graphs for (a) and (c) appear on the same page. The graphs for (c) are shown as dashed lines.

Graphs for (b) and (d) appear on the same page. The graph for (d) is shown in orange (as a dashed line). All threee lines look exactly like this.

_____

Comment on the graphing program

These are graphed using the Desmos on-line graphing calculator. It has a tutorial available and is not difficult to learn for most simple graphing applications. (It prefers the variables x and y.) Graphs can be saved for later. (Here, screen shots are used because Brainly doesn't like external links.)

To find the x-intercept, set y=0 and solve.

... 0 = log(12x +7) -3

... 3 = log(12x +7) . . . . add 3

... 1000 = 12x +7 . . . . take the antilog. (10^3 = 1000)

... 993 = 12x . . . . . . . .subtract 7

... 82.75 = x . . . . . . . . divide by 12

To find the y-intercept, set x=0 and solve.

... y = log(12·0 +7) -3

... y = log(7) -3 . . . . . . simplify

... y ≈ 0.85 -3 = -2.15 . . . . use a calculator for the log function

[tex]0.5x+\dfrac{7}{8}=5\qquad\text{multiply both sides by 8}\\\\4x+7=40\qquad\text{subtract 7 from both sides}\\\\4x=33\qquad\text{divide both sides by 4}\\\\\boxed{x=\dfrac{33}{4}\to x=8\dfrac{1}{4}}[/tex]

C. None of the above

It appears to me the average times for Ravens backs are lower (< 4.44 s) than those of Chiefs backs (< 4.48 s), so the Ravens are faster on average.

The spread of Ravens times is 4.30–4.57 s, whereas the spread of Chiefs times is 4.42–4.56. The Ravens clearly show a greater variation.

The offered choices suggest the Chiefs are faster on average (not true) and that the Chiefs have a greater variation (not true). Since both of these choices are incorrect, the only remaining suitable choice is None of the above.

Answer:

-7(x-5)= y+9

Its kind of hard to explian but...

Hope this helped!! Have a good day c;

Answer:y-6=-7(x-3)

Step-by-step explanation:(3,6) and 5,-8)

Slope= -8-6/5-3

= -14/2

= -7

If your equation started out like this: y-6= then you need to use the point (3,6):

y-6=-7(x-3)

the second degree term of the expression x^2 + 12x arrowRight the area of the culture banner

the first degree term of the expression x^2 + 12x arrowRight the increase in area of the culture banner to make the sports banner

the monomial, x, a factor of the expression x^2 + 12x arrowRight the width of the sports banner

the binomial, (x + 12), a factor of the expression x^2 + 12x arrowRight the length of the sports banner

The problem statement tells you x is the side length of the culture banner, and also the side length of the sports banner. It also tells you the length of the sports banner is 12 (inches) more than that of the culture banner, a value that can be written as x+12.

Of course, the area of a rectangle is the product of its length and width dimensions. Since the culture banner is a square of side length x, its area will be x^2. Since the sports banner is 12 inches longer and still x inches wide, the increase in area that represents will be 12x.

Answer with explanation:

3.19 =There are two digits after decimals.

An integer is set of numbers which includes both positive natural number, Negative Natural number and Zero.

[tex]3.19=\frac{319}{100}[/tex]

Here, 319 and 100 , both are integers.

You can write equivalent form of

[tex]\frac{319}{100}=\frac{319 \times 2}{100 \times 2}=\frac{319 \times 3}{100 \times 3}=........[/tex]

The value 3.19 expressed as a ratio of two integers is :

[tex] \frac{319}{100} [/tex]

Given the decimal :

3.19 which can be expressed as an integer by multiplying with the Number of decimal places after the decimal Point.

To express 3.19 as a combination of two integer values, we divide 319 by 100

Hence, 3.19 = 319 ÷ 100

[tex] \frac{319}{100} [/tex]

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Answer:

"earn"

Step-by-step explanation:

He paid $9 for a box of 24 pens. Selling those 24 pens for $1 each, he sold them for $24. Thus he earned $24 -9 = $15 on each of the 8 boxes he bought.

Answer:

39

Step-by-step explanation:

Let a and b represent the first and second digits, respectively.

... a = b -6 . . . . . . the first digit is 6 less than the second

... a + b = 12 . . . . .the sum of digits is 12 (an even number)

Using the expression in the first equation, we can substitute for a in the second equation:

... (b -6) +b = 12

... 2b = 18 . . . . . . add 6, simplify

... b = 9 . . . . . . . . .divide by 2

... a = 9 -6 = 3 . . . . from the first equation

The number is 39.

If you travel at a constant speed, you follow this equation:

[tex] d = st [/tex]

where d is the distance, s is the speed and t is the time.

In this example, you first travel 60 miles per hour for 45 minutes. Since 45 minutes are 3/4 of a hour, you will cover a distance of

[tex] d_1 = 60\cdot\dfrac{3}{4} = 45 [/tex]

In the second part, since 30 minutes is half a hour, you will cover a distance of

[tex] d_2 = 50\cdot\dfrac{1}{2}=25 [/tex]

So, in total, you travel

[tex] d=d_1+d_2=45+25 = 70 [/tex] miles

Answer:

C-70 miles

Hope this helped :)

Answer:

33

Step-by-step explanation:

I think it would be 33 bc if you subtract 90-66 its 33 but

how did i get 90 bc 90 is a right angel.  

Answer:

(53.35/11)*4=19.40

Step-by-step explanation:

The cost of 4 key chains is $19.40.

Cost per key chain = Total cost / Number of key chains

                                 = $53.35 / 11

                                   ≈ $4.85

Cost for 4 key chains = Cost per key chain * 4

                                     = $4.85 * 4

                                     = $19.40

So, 4 key chains cost $19.40.

Answer:

12 years

Step-by-step explanation:

r = compound interest rate in percent

t = doubling time in years

t = (72percent years)/(6 percent) = 12 years

As a curious cultural fact, there is a connection between the 72 and the fact that ln(2) = 0.69314718055. The constant is 69.3 for continuous compounding...

Answer:

12 years

Step-by-step explanation:

Answer:

y = ln(x -5)

Step-by-step explanation:

The log function has a vertical asymptote at x=0 and goes through the point (1, 0). This looks like that function translated 5 units to the right. When f(x) is translated right 5 units, x is replaced by x-5. The graph seems to be of the function ...

... y = ln(x -5)

_____

The natural log function will go through the points (2.718, 1) and (7.389, 2), as this curve appears to do.

Answer:

$217.07

Step-by-step explanation:

Each year, the cost of the groceries was multiplied by 100% +2.7% = 1.027. Doing this multiplication for 5 years result in a multiplying facor of ...

... 1.027^5

so the cost of the groceries after 5 years is ...

... $190.00 × 1.027^5 ≈ $217.07

Answer:

B

Step-by-step explanation:

[tex]5\cdot 21^{5x} = 16 \\\ 21^{5x} = \frac{16}{5} \\\\ 21^{5x} = 3.2 \\\ log 21^{5x} = log 3.2 \\\ 5x\cdot log 21 = log 3.2 \\\ 5x = \frac{log 3.2}{log 21} \\\\\ x = \frac{log 3.2}{5\cdot log 21}[/tex]

I hope I helped you.