Solve and graph each of the following. Show your work to receive full credit.5x – 6 – 8x ≤ 9

point A will represent the input-output values of the function.

What is number line ?

Number line is virtual representation of numbers along with coordinates axis with number equally spaced with equal number of interval.

In the graph of y = f(x),

For every x-value (input value), value of the function is the y-value (output value).

For the input value x = 2,

Output value of the function will be,

y = f(2)

Therefore, point A will represent the input-output values of the function.

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Johnny's assumption is that, none of the residents of the town will live up to 231 years.

The parameters are given as:

[tex]\mathbf{P_o = 10000}[/tex]--- the population in 2005

[tex]\mathbf{r = 0.3\%}[/tex] -- the rate at which the population declines

To model a population, we make use of the following exponential function

[tex]\mathbf{P = P_o \times(1 -r)^t}[/tex]

Where P is the current population in t years.

So, we have:

[tex]\mathbf{P = 10000 \times(1 -0.3\%)^t}[/tex]

When the population reaches half of the initial population, then P = 5000.

So, we have:

[tex]\mathbf{5000 = 10000 \times(1 -0.3\%)^t}[/tex]

Divide both sides by 10000

[tex]\mathbf{0.5 = (1 -0.3\%)^t}[/tex]

[tex]\mathbf{0.5 = (0.997)^t}[/tex]

Take logarithm of both sides

[tex]\mathbf{log(0.5) = log(0.997)^t}[/tex]

Rewrite the equation as

[tex]\mathbf{log(0.5) = tlog(0.997)}[/tex]

Make t the subject

[tex]\mathbf{t = \frac{log(0.5)}{log(0.997)}}[/tex]

[tex]\mathbf{t = 231}[/tex]

This means that the population will halve its initial population in 231 years.

Johnny's assumption is that, none of the residents of the town will live up to 231 years.

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Answer:

Slope = ½

Step-by-step explanation:

Given the two points on the graph, (-4 , 0) and (0, 2):

Let (x₁, y₁) = (-4 , 0)

      (x₂, y₂) = (0, 2)

Substitute the given points into the following slope formula:

[tex]\LARGE\mathsf{m = \frac {(y_2\: -\: y_1)}{(x_2\: -\: x_1)}}[/tex]

[tex]\LARGE\mathsf{m = \frac {2\: -\:0}{0\: -\:(-4)}}[/tex]

[tex]\LARGE\mathsf{m = \frac {2\: -\:0}{0\: +\:4}}[/tex]

[tex]\LARGE\mathsf{m = \frac {2}{4}\:=\:\frac{1}{2}}[/tex]

Therefore, the slope of the line is ½.

Answer:

k

Step-by-step explanation:

3k-2k=1k

1k=k so this is the answer

Answer:

5

Step-by-step explanation:

it is half of ten which is 5

Hope this helps

Answer:

top one is correct I think

Answer: 6

Step-by-step explanation:

Let's look at two points on this line (1, 5), and (0, -1)

Using the slope formula ([tex]\frac{y_2-y_1}{x_2-x_1}[/tex])

[tex]\frac{((5) - (-1))}{(1)-(0)}[/tex]

[tex]\frac{6}{1}[/tex]

Hope it helps :)

Answer:

Well you could count and use the Rise/Run method, or you could use the Slope formula (x2 - x1) / (y2 - y1)

From point (0, -1) to point (1, 6) would look like this

(1 - 0) / (6 + 1) = 1/7, so your slope is 1/7

Since you already have you y-intercept (where x is 0), your whole equation would be this:

y = 1/7x - 1

Answer:

a = 16

Step-by-step explanation:

The median is the middle value of the data arranged in ascending order.

If there is no exact middle then the median is the average of the 2 values either side of the middle

a + 1 , 2a - 1 ,  a + 7 ,  3a + 4

                   ↑ middle

Then

[tex]\frac{2a-1+a+7}{2}[/tex] = 27 ( multiply both sides by 2 to clear the fraction )

3a + 6 = 54 ( subtract 6 from both sides )

3a = 48 ( divide both sides by 3 )

a = 16

Answer:

I couldn't decipher your question heres a graph for https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7984252/

that contains quartile ranges of stored bananas

Step-by-step explanation:

If this doesn't help please correct your question or tell me more so I can better help you

(36.39- 2.99)/20

Total- chips, so total amount for juice.

Then, divide by 20 because she bought 20 bottles

Answer:

1.67

Step-by-step explanation:

36.39 - 2.99 = 33.4 33.4 ÷ 20 = 1.67

Answer:

The casino is making 47 cents profit on your $1 bet

Step-by-step explanation:

19(1/38) + (-1)(37/38) = -0.4736

Answer:

do I need to answer the questions in every pic?

Answer:

open the ones in bracket first

(_6)2 = _ 36

Step-by-step explanation:

so there fore 26.08 + (- 36) + 3.4 - 8.9 ÷ 9

open bracket by multiplying the signs

which implies

26.08 - 36 + (3.4 - 8.9) ÷ 9

- 9 .92 + (- 5.5) ÷ 9

open brackets by multiplying the signs

-9.92 - 5.5 ÷ 9

- 15.42 ÷ 9

which will give -1.713 approximately

Answer:

x=3 and y= 4 / 3 (Fraction)

Step-by-step explanation:

Substitute x for 6y-5.

2(6y−5)−3y=2

Add 6y and 3y, and multiply 5 by 2/Simplify the equation.

9y−10=2

Add  10 to both sides, and then divide each side by 9.

9y−10+10=2+10

9y / 9 = 12 / 9

y = 4/3.

Repeat the process but replace y with 4/3!

Answer:

x=3

y= 4/3

Step-by-step explanation:

2(6y-5)-3y=2

y= 4/3

x=6x 4/3-5

x=3

Answer:

Step-by-step explanation:

18.

LHS

[tex]\frac{cos^{2}a-sin^{2}b }{sin^{2}a.sin^{2}b}[/tex]

= [tex]\frac{cos^{2}a }{sin^{2}a.sin^{2}b} -\frac{sin^{2}b }{sin^{2}a.sin^{2}b}[/tex]

= [tex]\frac{cos^{2}a}{sin^{2}a}[/tex] × [tex]\frac{1}{sin^{2}b}[/tex] - [tex]\frac{sin^{2}b}{sin^{2}b}[/tex] × [tex]\frac{1}{sin^{2}a}[/tex]

= [tex]cot^{2}a[/tex] × [tex](1+cot^{2}b)[/tex] - 1 × [tex](1 + cot^{2}a)[/tex]

= [tex]cot^{2}a[/tex] + [tex]cot^{2}a.cot^{2}b[/tex] - 1 - [tex]cot^{2}a[/tex]

= [tex]cot^{2}a.cot^{2}b[/tex] - 1

Then you can conclude that LHS = RHS

19. It's weird. I tried a few ways like simplifying, dividing both numerator and denominator on LHS by tan or sin or cos but it didn't work out.

Hey there!

I'm going to go in order from images.

1. The angle measure 60 is linear to angle 6, this would make them supplementary.

Angle 6: 180 - 60 = 120

Angle 6 is vertical to angle 2, this makes them congruent. If angle 6 equals 120 measure 2 also equals 120.

2. Measure 6 is vertical from measure 2. We established in the last problem measure 2 equals 120.

If angle 2 equals 120 measure 6 also equals 120.

3. The 2 equations are alternate exterior angles.

2x+5=8x-7

    +7     +7

2x+12=8x

-2x     -2x

12=6x

12/6= 2

x=2

4. I cannot explain this one without showing it visually lol.

Measure 5 equals 30 degrees.

5. Measure 1 is verticle to the measure that reads 60. Vertical angles are congruent.

If measure 1 is congruent to the measure that reads 60. Measure 1 equals 60.

I hope this helps!!!

Answer:

d=7

Step-by-step explanation:

7-2.125= 4.875

7 is your answer as it balances both sides of the equation.

i got seven by adding 2.125. to 4.875

Answer:

Step-by-step explanation:

1. add 2.125 to both sides of your equation

4.875 = d - 2.125

+2.125        +2.125

7 = d

The d is now isolated which allows us to see the answer is 7 for d

Answer:

x=–4, y=1

Step-by-step explanation:

adding the 2 equations, we see the X's go away and we are left with: 10y=10. we can simplify and solve for y by dividing both sides by 10 and we are left with y=1

plugging 'y=1' into the fist equation we get: -7x+6=34. we can now solve for x by subtracting 6 from both sides and dividing both side by –7, so we are left with: x=–4

we can check by plugging both x and y into one of the original equations:

-7(-4)+6(1)=34

28+6=34

34=34✓

Answer:

C) y = 3x + 2

Step-by-step explanation:

Given the slope of the line, m = 3, and the coordinates of the y-intercept, (0, 2).

We can substitute these values into the following slope-intercept form, y = mx + b, where:

m = slope

b = the y-coordinate of the y-intercept.

Therefore, the correct answer is option C, where it shows the equation of the line in slope-intercept form is: y = 3x + 2.

[tex]5y-3 = -23\\\\\implies 5y = -23 +3 = -20\\\\\implies y = -4[/tex]

Answer:

195,500,000 people.

Step-by-step explanation:

8.5 mil times 23 equals 195,500,000

Answer:

4.6x10^6

Step-by-step explanation:

4.6x10^6=46000000

we have 5^4 . (5^-2)^3 = 5^4 . 5^-6 = 5^ (4-6) = 5^-2

ok done. Thank to me :>

Answer:6

Step-by-step explanation:

Step-by-step explanation:

the vertex is the point, where the parabola turns around. it is (depending on its orientation, if it is opening upwards or downwards) the maximum or the minimum of the curve.

so, as we can see on the grid, that point is x = -3, y = +1 = (-3, 1).

so, B is correct

Answer:

B. (−3, 1)

Step-by-step explanation:

-3, 1 is the vertex I believe

-3,1 should be the one

Answer:

x = (8+t)/d

Step-by-step explanation:

Since you want to make x the subject of the formula, you would want it along. so you should move the t to the other side, which will get you dx = 8+t, then you will have to divide both sides by d to get the x along, and in this case, you will get x = (8+t)/d

The given formula can be written as x = (8 + t)/d.

A linear equation in two variable has the general form as y = ax + by + c, where a, b and c are integers and a, b ≠ 0.

It can be represented as a straight line on a graph.

The given formula is as below,

dx - t = 8

Since, it is a linear equation with variable x. It can be rewritten as follows,

dx - t = 8

=> dx = 8 + t

=> x = (8 + t)/d

Hence, by making x as the subject the given formula becomes as x = (8 + t)/d.

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Answer:

min: (-2;-6) & (1; 3/4); max: (0;2).

Step-by-step explanation:

1) f`(x)=3x³+3x²-6x;

2) f`(x)=0, ⇒ 3x³+3x²-6x=0;

3) 3x³+3x²-6x=0; ⇒ x(x²+x-2)=0; ⇒ x(x-1)(x+2)=0; ⇒ x₁=0; x₂=1; x₃=-2;

other steps are provided in the attachment.

Answer:

3:10

Step-by-step explanation:

Disposal time=1:15PM

Choir ending time:-

[tex]\\ \sf\longmapsto 1:15-0:40=12:35PM[/tex]

Answer:

Triangle A'B'C'

A'B'= 7.81

B'C'= 6

A'C'=5

C) Perimeter= 18.81 Area 15

Triangle ABC

AB=5

BC=4

AC=3

c) Perimeter = 12 Area = 6

Step-by-step explanation:

Triangle ABC work

Perimeter 4+3+√4^2+3^2=12

Area  4*3/2=6

Triangle A'B'C' work

Area 6*5/2=15

Perimeter 6+5+√6^2+5^2=18.81025

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