17.
Write the equation in standard form. Then factor the left side of the equation.

2x2 + 7x = 15


A. (2x – 5)(x + 3) = 0

B. (2x + 3)(x + 5) = 0

C. (2x – 3)(x + 5) = 0

D. (2x + 5)(x – 3) = 0

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.

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:

Answer:

39

Step-by-step explanation:

Answer:

A picture of the graph is attached

Step-by-step explanation:

Answer:

24a²-73ab+24b²

Step-by-step explanation:

(8a - 3b) (3a - 8b) =

24a²-64ab-9ab+24b²

= 24a²-73ab+24b²

Answer:

hiii my pic lol (✿^‿^)(✿^‿^)(✿^‿^)(✿^‿^)

Answer:

Step-by-step explanation:

The exponential decay function is

[tex]v(t)=a(b)^t[/tex] where b, the rate of decay, for us is (1 - .115) and a is the original value of the car which, for us, is 18000. t is the time in years. Using this information to write the equation we need to solve for the value when the car is 10 years old:

[tex]v(t)=18000(.885)^t[/tex] and we sub in 10 for t:

[tex]v(t)=18000(.885)^{10[/tex] which simplifies to

v(t) = 18000(.2947356754) so

v(t) = 5305.24

48 ÷ (7 x 5 - 3 x 9)

= 48 ÷ (35 - 27)

= 48 ÷ 8

= 6

Step-by-step explanation:

only half of your points for each answer ;)

Answer: 6

Step-by-step explanation:

Because of PEMDAS, you do 7x5 which is 35 than 3x9 which is 27. Then you subtract those and get 8. After you finish what's in the parenthesis, you divide 48 by 8 which is 6.

Answer:

17.1972degrees

Step-by-step explanation:

length of an arc = theta/360 * 2πr

Substitute the given angle;

1.2 = theta/360 * 2(3.14)(4)

1.2 = theta/360 * 25.12

1.2/25.12 = theta/360

0.04777 = theta/360

theta = 360 * .04777

theta = 17.1972

Hence the required angle is 17.1972degrees

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:

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

Answer:

d

Step-by-step explanation:

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:

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

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:

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:322.64 (I think)

Step-by-step explanation:

550-227.36=322.64

Answer:

what the other person said here

Hi there!

[tex]\large\boxed{\text{Gradient = -1}}[/tex]

We can find the slope using the slope formula:

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

Plug in the given coordinates:

Slope = (1 - 5)/(7 - 3)

Simplify:

Slope = -4/4

Slope = -1

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:

she will make 78 dollars

Step-by-step explanation:

312 divided by 24 is `13

13 times 6 is 78

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:

Option C

Step-by-step explanation:

Barrel (storage container) is enclosed in a small square fence.

Since, barrel is touching the surfaces from four sides of the cylindrical barrel.

Length of each side of the square fence = Diameter of the barrel

                                                                   = 2(radius of the barrel)

                                                                   = 2(1.5)

                                                                   = 3 feet

Perimeter of a square = 4(Side of a square)

                                     = 4(3)

                                     = 12 feet

Therefore, Option C will be the correct option.

Answer:

63462 pies

Step-by-step explanation:

De la pregunta anterior, debemos encontrar el área del sector

La fórmula se da como:

θ / 360 × πr²

Dónde:

θ = 45 °

radio = 402 pies

Área del sector =

45/360 × π × 402²

= 63461.742399 pies

Aproximadamente el área de la ocupada por el parque = 63462 pies

Answer:

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

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).