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Answer:

909 and 3267

Step-by-step explanation:

There are a total of 24 possible combinations using these 4 digits. This means that any one of these combinations subtracted from 4310 would be a possible solution. Therefore, we can create the following 2 combinations (below in bold) and subtract them from 4310 to get two possible solutions...

4310 - 3401 = 909

4310 - 1043 = 3267

Finally, we have two possible solutions which would be 909 and 3267

Answer:

Two real distinct solutions

Step-by-step explanation:

Hi there!

Background of the Discriminant

The discriminant [tex]b^2-4ac[/tex] applies to quadratic equations when they are organised in standard form: [tex]ax^2+bx+c=0[/tex].

All quadratic equations can be solved with the quadratic formula: [tex]x = \frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}}[/tex].

When [tex]b^2-4ac[/tex] is positive, it is possible to take its square root and end up with two real, distinct values of x.

When it is zero, we won't be taking the square root at all and we will end up with two real solutions that are equal, or just one solution.

When it is negative, it is impossible to take the square root and we will end up with two non-real solutions.

Solving the Problem

[tex]3x^2+5x=-1[/tex]

We're given the above equation. It hasn't been organised completely in [tex]ax^2+bx+c=0[/tex], but we can change that by adding 1 to both sides to make the right side equal to 0:

[tex]3x^2+5x+1=0[/tex]

Now that we can identify the values of a, b and c, we can plug them into the discriminant:

[tex]D=b^2-4ac\\D=(5)^2-4(3)(1)\\D=25-4(3)(1)\\D=25-12\\D=13[/tex]

Therefore, because the discriminant is positive, the equation has two real, distinct solutions.

I hope this helps!

Answer:

The maximum height that the stone reaches is of 26 feet.

Step-by-step explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

[tex]f(x) = ax^{2} + bx + c[/tex]

It's vertex is the point [tex](x_{v}, y_{v})[/tex]

In which

[tex]x_{v} = -\frac{b}{2a}[/tex]

[tex]y_{v} = -\frac{\Delta}{4a}[/tex]

Where

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

If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].

y = -2x2 + 8x + 5

Quadratic function with [tex]a = -2, b = 8, c = 5[/tex]

What is the maximum height that the stone reaches?

y value of the vertex. So

[tex]\Delta = 8^2-4(-2)(5) = 64 + 40 = 104[/tex]

[tex]y_{v} = -\frac{104}{4(-2)} = 26[/tex]

The maximum height that the stone reaches is of 26 feet.

X = 3-2^2

Simplify x:

3-4 = -1

X = -1

Replace x in the equation and solve:

(-1) ^2 + 1 /(-1)^2

(-1)^2 = 1

Simplify to get 1 + 1/1 = 1+ 1 = 2

The answer = 2

Answer:

x = 74.4

Step-by-step explanation:

tan = opp/adj

tan42 = 67 / x

x = 67/tan42

use calculator

x = 74.411038493555922

rounded

x = 74.4

Answer:

A, B, and D

Step-by-step explanation:

Thanks! But what is it for??

Answer:

Thanks I got my free thing from this code that points out where to redeem it

Step-by-step explanation:

Answer: 3275

Step-by-step explanation:

Answer:

A picture of the graph is attached

Step-by-step explanation:

Answer:

Step-by-step explanation:

the formula is C=2√πA

so simplifying that would give us c=2(4π)

simplify again and we get c=8π

Answer:

97,988.216

Step-by-step explanation:

So, we can find this by using the following formula:

First value(change)^time

We know that the orginal, or first value, is 120,000.

We know that the time interval for this is 8 years, which is our time value.

We know that the decrease in this price is 2.5%. However, this is not our change.

Our change is the 97.5% price that is left.

This makes sense, because you would get a super small price when you use 2.5% as change.

So to sum up what we have done so far:

First value - 120,000

Change - 100%-2.5% = 97.5%. In decimal form: 0.975

Time - 8

So lets plug these into:

[tex]First_.value(change)^t^i^m^e[/tex]

=

[tex]120,000(0.975)^8[/tex]

And remember your order of operations here.

We dont have any equations or expressions inside the parethese, so we can move on to what comes next - exponents.

We have the exponent 8, which is attached to the 0.975.

So in your calculator, take 0.975, and put it to the 8th power.

You should get 0.816651803662261962890625

Lets leave it like this, becuase 120,000 is a very large value, and rounding what you multiply could change what you get in the end.

Now  our equation looks like:

120,000(0.816651803662261962890625)

We have done parethese, exponents - now we have multiplication and division.

We do indeed have this, since 120,000(0.816651803662261962890625) could also be written as:

[tex]120,000*0.816651803662261962890625[/tex]

Now multiplying this you should get:

97,998.216439471435546875

This is where you can round your answer.

I do not know what exactly they want you to round to, so its safe to just round your answer to the hundreths place:

97,998.22

So this is the new price of the car!

Hope this helps!

oh I did a mistake earlier , pardon ^^"

Let price after 8 years be P.

Using the compound interest formula of shrinking principal :-

P = Pₒ( 1 - R/ 100) ᵀ

P = 120, 000 ( 1 - 2.5/ 100)ᵀ

P = 120, 000 { (100 - 2.5)/ 100}ᵀ

P = 120, 000{ 97. 5/ 100 }ᵀ

P = 120, 000 {0. 975 } ⁸

P = 120, 000 { 0. 8166}

P = 97,998.216 $

Since, P is is price after 8 years

The price of the car after 8 years will be 97, 998. 216 $

Answer:

The answer is below

Step-by-step explanation:

1) Average speed is the ratio of the total distance travelled to the total time taken. Hence it is given by:

Average speed = total distance / total time

Total distance = d miles + w miles

Jacqui drives three times as long as she walks during the trip, hence:

time spent driving = 3t

Total time = 3t + t

Average speed = total distance / total time

a = (d + w) / (3t + t)

2) (3t + t) represents the total time that Jacqui spends traveling to the beach.

3) Given that a = 36 miles per hour, total time = 2 hours

a = total distance / total time

36 miles per hour = total distance / 2 hours

total distance = 72 miles

Total distance = distance walk + distance drove

72 = distance walk + 70

Distance walk = 2 miles

Answer:

[tex]\frac{x}{3} + \frac{1}{1} = \frac{x+3}{3}[/tex]

Step-by-step explanation:

[tex]\frac{x}{3} + \frac{1}{1} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ LCM \ of \ 1 , 3 = 3 \ ]\\\\= \frac{x}{3} + \frac{1 \times 3}{1 \times 3} \\\\= \frac{x}{3} + \frac{3}{3}\\\\=\frac{x+ 3}{3} \\\\[/tex]

Answer:

Step-by-step explanation:

Probability is 1/36.

The probability is defined as the possibility of an event to happen is equal to the ratio of the number of outcomes and the total number of outcomes.

Two dices were rolled.

Total outcomes in sample space: S = 36

Outcomes which have sum as 12 are E = {(6,6)}

Required Probability: P(E)= 1/36

Hence, Probability is 1/36 of which have sum as 12

Learn more about Probability

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Answer:

1/36

Step-by-step explanation:

Answer:

A: less that

Step-by-step explanation:

4( 14)+3

36+3= 39

39 (2+9)6-7

(11)6-7

66-7

59

39<59

Answer:

pretty sure its positive

Step-by-step explanation:

hope this helps, have  a great day!

Answer:

A is correct

Step-by-step explanation:

if we know that both x and y are positive, they are both going to be negative

and since we know that, -x divided by -y is the same as saying something negative divided by something negative which is ALWAYS positive because negatives cancel out leaving the answer positive something, something

Step-by-step explanation:

1) y = -x+4

2) y-4= -2(x-3)

y = -2x+6+4

y = -2x+10

3) slope = (3+1)/(9-1) = 4/8=½

the Equation =>

y+1= ½(x-1)

y = ½x -½-1

y = ½x - 1½ or 2y = x -3

Answer:

2r5r

jr = 986 which is 459=100 equals wrong

The factorization of the given expression [tex]55z^{17}+121z^{34}[/tex] is [tex]11z^{17}(5+11z^{17})[/tex].

"Factorization is a method of finding factors for any polynomial or any algebraic expression."

The given expression is

[tex]55z^{17}+121z^{34}[/tex]

By factorizing it, we get:

[tex]55z^{17}+121z^{34}\\= 11z^{17}(5+11z^{17})[/tex]

Learn more about factorization of an expression here: https://brainly.com/question/11994062

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Answer:

5/27

30/81 = 10/17

it's just ratios but if you need then vice versa, swap numerator and denominator

Answer:

the person on top is correct :)

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

To find the inverse of a function, first replace f(x) with y.

Next, switch all the x's and y's, and then solve for y.

Finally, replace y with f-1(x).

Answer:

-6

Step-by-step explanation:

since x = - 5 is < 3

for x < 3,

f(x) = 3x + 9

placing the value of x as - 5

f(x) = 3× (-5) + 9

= -15 + 9

Answer:

( x+3 )² = 7

expand ( x+3 )² : x²+6x+9

x²+6x+9=7

x²+6x+2=0

use a scientific calculator casio mode setup click no 5 , then click 3 input the equation

a = 1

b = 6

c = 2

answer : x = -3+square root 7 or x = -3-square root 7

Answer:

$8.39 por pe rsona

Step-by-step explanation:

Question:

ABCD is a trapezium in which AB ∥ CD, AD ⊥ DC, AB = 4 cm, BP = 7 cm and DC = 25 cm, then area of the trapezium is ____.

Answer:

101.5cm²

Step-by-step explanation:

The figure for the trapezium ABCD is attached to this response.

To find the area of the trapezium, we use the formula for calculating the area of a trapezium given as follows;

A  = [tex]\frac{1}{2}[/tex] x (a + b) x h            ------------------(i)

Where;

A = area of the trapezium

a and b are the parallel sides of the trapezium

h = height of the trapezium.

As shown in the figure,

AB and CD are parallel

Therefore, we can say that;

a = AB

b = CD

Also, from the figure,

The height of the trapezium is BP

Therefore, we can say that;

h = BP

We know that;

a = AB = 4cm

b = CD = 25cm

h = BP = 7cm

Substitute these values of a, b and h into equation (i) as follows;

A  = [tex]\frac{1}{2}[/tex] x (4 + 25) x 7    

A  = [tex]\frac{1}{2}[/tex] x (29) x 7    

A = 101.5

Therefore, the area of the trapezium is 101.5cm²

Answer:

5

Step-by-step explanation:

Let a = number of pieces of chocolate bought by Amin.

Let b = number of pieces of chocolate bought by Bob.

b = 2a

(a - 3)(b - 3) = 14

ab - 3a - 3b + 9 = 14

a(2a) - 3a - 3(2a) = 5

2a^2 - 3a - 6a = 5

2a^2 - 9a - 5 = 0

(2a + 1)(a - 5) = 0

2a + 1 = 0  or  a - 5 = 0

a = -1/2  or  a = 5

Amin cannot have bought -1/2 pieces of chocolate, so we discard the soluion a = -1/2.

a = 5

Answer: 5

Answer:

ok so for g times h you would have to foil it and then you would multiply it by f of X

Answer:

5 grams/metres squared = 50 kg/hectares

Step-by-step explanation:

We need to convert 5 grams/metres squared to kilograms/hectares.

We know that,

1 kg = 1000 g

1 hectare = 10000 m²

So,

[tex]5\ \dfrac{g}{m^2}=5\times \dfrac{0.001}{\dfrac{1}{10000}}\\\\=50[/tex]

Hence, 5 grams/metres squared = 50 kg/hectares

Answer:

she will make 78 dollars

Step-by-step explanation:

312 divided by 24 is `13

13 times 6 is 78

Answer:

16

Step-by-step explanation:

f(x) = (-4 + x)^2

Let x=8

f(8) = (-4 + 8)^2

Parentheses  first

     = 4^2

Then powers

    = 16