For the following quadratic equation, find the discriminant. –4x² + 24x – 152 = 0
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The population of Ohio will be 10 million in the year 1970

The population growth of Ohio is represented by the function:

[tex]P(t)=\frac{12.79}{1+2.402e^{-}0.0309t}[/tex]

P is the population in millions

t is the number of years since 1900

To find the year that the population of Ohio will be 10 million, substitute P = 10 into the function P(t) and solve for t

[tex]10=\frac{12.79}{1+2.402e^{-}0.0309t}\\\\10(1+2.402e^{-}0.0309t)=12.79\\\\1+2.402e^{-}0.0309t=\frac{12.79}{10} \\\\1+2.402e^{-}0.0309t=1.279\\\\2.402e^{-}0.0309t=1.279-1\\\\2.402e^{-}0.0309t = 0.279\\\\e^{-}0.0309t =\frac{0.279}{2.402} \\\\e^{-}0.0309t =0.116\\\\-0.0309t=ln0.116\\\\-0.0309t=-2.154\\\\t=\frac{-2.154}{-0.0309} \\\\t=69.7[/tex]

t = 70 years (to the nearest whole number)

70 years after 1900 will be 1970

Therefore, the population of Ohio will be 10 million in the year 1970

Learn more here:  https://brainly.com/question/25504185

Answer:

Step-by-step explanation:

28 > 6x - 2

28 + 2 > 6x - 2 + 2

30 > 6x

5 > x or x < 5

Answer:

268.25

Step-by-step explanation:

by using the fact that one year is 365.25 days, we can subtract our 365.25 by our 97 to get 268.25, written in the equation of 365.25-97=268.25

*edit, messed up how long a year was, corrected my issue, answer & equation.

Answer:

Step-by-step explanation:

How many did not rain is 268 because if you take away 97 from 365 ofcourse it will be 268 you’re welcome

Answer:

-4,2

Step-by-step explanation:

(x-2) (x+4)=0

x-2=0

x=2

x+4=0

x= -4

Answer:

x=-4, x=2

Step-by-step explanation:

Whenever a question asks you to find the zeros of a quadratic equation, they are essentially asking you to find the x-intercepts. To find the x-intercepts, you simply need to equate y to zero and solve for x.

There are two main ways to find the intercepts - by the quadratic formula and factoring. I will demonstrate both below.

When factoring, a popular method is the diamond box method. First, make an x on your paper. In the top nook of the x, write the product of a and c in y=ax^2 +bx +c. Here, it is -8*1=-8. In the bottom nook, write the b value. Here it is 2. Find two numbers that multiply to ac or -8 and add up to b or 2 and write them in the side nooks. In this problem, they are 4 and -2 (4*-2=-8 and 4+(-2)=2). Then, make a box. On the top left corner, write the first term (here it is x^2) and on the bottom right corner write the constant term (here it is -8) and write the two values you found earlier in the remaining boxes. Now, find values that multiply to each of the respective terms. Sorry, this sounds super confusing, I have included a picture below of what the result should look like. Once you have it factored, make y equal to zero and solve for both x's. You should get x=2 and x=-4. Keep in mind, sometimes, a problem might not be factorable. If it isn't, you have to use the method below.

Another popular way to find the roots is the quadratic formula. I have included a picture of it below. All you have to do is substitute the coefficients in and solve for x. You should get two solutions in this scenario.

Answer:

Please I don't understand the question or maybe I'm too young for the question I'm so sorry

Answer:

$4811

Step-by-step explanation:

Initial price = 35,000

18% decrease anually = 18/100 = -0.18

after 10 years

substitute these values in the formula shown in below figure

A = 35000 * ( 1 + -0.18/1  ) ^10

= 35000 * 0.82^10

= 4,810.681

= $4811

Answer:

112

Step-by-step explanation:

8 days when fitted into a half (1/2) gives you 16

7 times 16 gives the answer of 112 (people needed)

Answer:

112 people to do it in 1/2 of a day

Step-by-step explanation:

7 · 8 = 56

56 ÷ ½ = 112 people to dig a ditch in 1/2 of a day

Answer:

x > -2

Step-by-step explanation:

As the circle in the number line is not filled, it will not include -2 and as the number line starts from -2 and goes right it will be x > -2.

Hope this helps!!

Answer:

25ml of wallpaper remover

Step-by-step explanation:

(y = amount of wallpaper remover)

4500×4 = 18000

18000:600

750    : y

18000y = 600×750

18000y = 450000

y = 450000÷18000

y = 25

Answer:

Below.

Step-by-step explanation:

1. Divide both sides by 2.

2. After dividing both sides by we would have:

x + 14 = 20

The next step would be

Subtract 14 from both sides.

3. 2(x + 14) = 40

x + 14 = 20

x = 20 - 14

x = 6.

2x + 28 = 40

2x = 40 - 28

2x = 12

x = 6.

Answer:

[tex]m=-\frac{1}{2}[/tex]

Step-by-step explanation:

Same as last time, take any 2 points you want:

(0, 3) and (4, 1)

Use the slope formula to calculate the slope:

[tex]m=\frac{1-3}{4-0}\\m=\frac{-2}{4}\\m=-\frac{1}{2}[/tex]

On small problems like these, you don't really even need to calculate it like that. You can just look at the graph, see that it goes down 1 and over 2 from one point to the next, and have your slope that way. Again, rise over run. It "rises" by -1, and runs by 2. -1 over 2, there's your slope.

Answer:

Step-by-step explanation:

Look at the first elements of the four points:  {0, 3, 6, 6}.  The element 6 appears twice and is associated with two different second elements:  {8, 12}.  That tells us immediately that this is not a function.

Answer:

37/8

Step-by-step explanation:

Find the GCD (or HCF) of numerator and denominator. GCD of 4625 and 1000 is 125.

4625 ÷ 1251000 ÷ 125.

Reduced fraction: 378. Therefore, 4625/1000 simplified to lowest terms is 37/8.

Answer:

29cm

Step-by-step explanation:

a radius is half of a diameter so half of 58cm  is 29cm.

i hope this helps have a good day

Answer:

[tex]x4 - (9x5)[/tex]

yan npo wag puro brainly

Answer:

The answer is l =40cm

Step 1: We have the next system of equations -

[tex]2x - 3y = 13[/tex]

[tex]x + 2y = 4[/tex]

Step 2: Now, we will multiply by -2 the second equation:-

[tex] - 2(x + 2y) = 4[/tex]

[tex]→ - 2x - 4y = - 8[/tex]

Step 3: Then we add it :-

[tex]2x - 3y = 13[/tex]

[tex]( + ) \: - 2x - 4y = - 8[/tex]

Step 4: After finding the sum, we simplify:-

[tex] - 7y = 5[/tex]

[tex]→y = - \frac{5}{7} [/tex]

Then, substitute the above y value to find x's value in any equation of Step 1. Now, I used to second equation in Step 1:-

[tex]x = - 2( \frac{ - 5}{7}) + 4[/tex]

Step 5: Then simplify :-

[tex]y = \frac{38}{7} [/tex]

Therefore, the final answer is :-

[tex]x = \frac{38}{7} [/tex]

and

[tex]y = \frac{5}{7} [/tex]

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Answered by Benjemin360 ☺️

Answer:

A = £1102.50

Step-by-step explanation:

Use the compound amount formula:

A = P(1 + r)^t, where P is the principal, r is the interest rate as a decimal fraction, and t is the number of years.

Here A = £1000·(1 + 0.05)^2, which evaluates to  A = £1102.50

Step-by-step explanation:

9.75/.75 = 13

which means the race is divided into 13 equal section according to the question in which each section is 0.75 m long.

as 4 volunteers are needed in each section

so keeping this in mind 13×4 = 52

therefore, 52 volunteers race organizer need.

hope this answer helps you dear! take care

Answer:

the answer is 15/17

because cosine=b/h=UV/UW=15/17

Answer:

Ram's neighbors probably had more apples than Ram.

Hence, number of apples in the neighbor's house is equal to [tex] \geqslant 5[/tex].

Step-by-step explanation:

Hello bro ufff.... Finally found u xD-,-

Answer:

y = 8x + 14  (8x is WRONG)

This is how it is supposed to be

y - 2 = 6x + 12

y = 6x + 14

She must combine like terms, not unlike terms

x=31/14

Step-by-step explanation:

I did the second one btw

Answer:

your answer is 1.65 or E :)

Answer:

it is (-4,1)

Step-by-step explanation:

Hope this helps:)

Answer:

I assume you are looking for the x and y values of the two equations? if not message me!

y=–2

x=1

Step-by-step explanation:

Multiply the first/top tearm by –3 so we can "get rid of" the X's with the addition of both equations. we are then left with: 14y=-28

We can now divide both sides by 14 to get y by itself so we are left with: y=–2

plugging our y value back into the first equation we get: 3x+8=11. we subtract 8 from both side and are left with: 3x=3. dividing both side by 3 we can get x by itself and are left with: x=1

To check, we plug x and y both into the first equation we get: 3+8=11 (which it does). Or we can plug both of them into the second equation and we get:9-4=5 (which it does)

Answer:

Below in bold.

Step-by-step explanation:

3x-4y=11

9x+2y=5

Multiply the first equation by 3:

9x - 12y = 33

Subtract the above from the second equation:

2y - (-12y) = 5 - 33

14y = -28

y = -2.

Now plug y = -2into the first equation:

3x - 4(-2) = 11

3x = 11 - 8 = 3

x= 1.

Answer:

0.4/1

Step-by-step explanation:

We want a unit rate where

1 is in the denominator,

so we divide top and bottom by 30