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3 years ago

(x – 4)(x + 10) = -17

Mathematics

1 answer:

pogonyaev3 years ago

4 0

Answer:

-3 + 4sqrt(2)

-3 - 4sqrt(2)

Step-by-step explanation:

(x – 4)(x + 10) = -17

FOIL on the left hand side (First outer inner last)

x^2 +10x-4x-40 = -17

x^2 +6x-40 =-17

Add 17 to each side

x^2 +6x-40+17 =-17+17

x^2 +6x -23 = 0

Using the quadratic formula

-b + - sqrt(b^2 -4ac)

-------------------------------

where ax^2 +bx+c=0

-6 + - sqrt(6^2 -4*1*-23)

-------------------------------

2*1

-6 + - sqrt(36 +92)

-------------------------------

-6 + - sqrt(128)

-------------------------------

-6 + - 8sqrt(2)

-------------------------------

Divide top and bottom by 2

-3 + - 4sqrt(2)

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Solve for x: 2 x + 10 + 2 x - 6 = 36

skad [1K]

Group together the like terms (plus 2x with 2x) (subtract 10 by 6)

4x+4=36

Move plus four to the other side as a negative

4x=32

Divide both sides by 4

32 divided by 4 is 8

Therefore, x is equal to 8

7 0

3 years ago

Solve the system of equations. Type in all points of intersection for the two functions and round to the nearest tenth if necess

Veseljchak [2.6K]

The points of intersection for the two functions and round to the nearest tenth are (0.5, 1.4) and (4.85, -0.3)

<h3>System of equations</h3>

Given the following function

f(x) = - 0.5x + 2

g(x) = x^3 - 5x^2 + 3

The point of intersection is the point where f(x) = g(x)

x^3 - 5x^2 + 3 = - 0.5x + 2

x^3 - 5x^2 + 3 + 0.5x - 2 = 0

x^3 - 5x^2 + 0.5x + 1 = 0

Factorize and determine the value of x

x = 0.53 and 4.85

If x = 0.53

f(0.53) = -0.5(0.53) + 2

f(0.53) = -0.265 + 2

f(0.53) = 1.375

If x = 4.85

f(4.85) = -0.5(4.85) + 2

f(4.85) = -2.425 + 2

f(4.85) = -0.245

Hence the points of intersection for the two functions and round to the nearest tenth are (0.5, 1.4) and (4.85, -0.3)

Learn more on functions here: brainly.com/question/10439235

#SPJ1

3 0

2 years ago

. Consumer Awareness In 1986, the average cost of a new midsize four-door sedan was $9000. In 1991, the average cost was $12,000

eduard

Answer-

$\boxed{\boxed{y=9000(1.0592)^x}}$

And cost of a car in the year 2000 will be $20134.18

Solution-

Let's assume,

x = number of years after 1986

y = average cost of sedan in dollar

The exponential model that will model the scenario will be in the form of,

$y=ab^x$

where a and b are constants

As given that, in 1986 average cost of sedan was $9000 and in 1991 average cost of sedan was $12000

So, the points (0, 9000) and (5, 12000) will satisfy or lie on the exponential curve.

Putting (0, 9000) in the equation,

$\Rightarrow 9000=ab^0$

$\Rightarrow a\times 1=9000$

$\Rightarrow a=9000$

Now, the equation becomes $y=9000b^x$

Putting (5, 12000) in this equation,

$\Rightarrow 12000=9000b^5$

$\Rightarrow b^5=\dfrac{12000}{9000}$

$\Rightarrow b=\sqrt[5]{\dfrac{4}{3}}$

$\Rightarrow b=1.0592$

Putting the values,

$y=9000(1.0592)^x$

As we have to calculate the cost of sedan in 2000, so putting x=14(as 2000-1986=14),

$y=9000(1.0592)^{14}=20134.18$

Therefore, cost of a car in the year 2000 will be $20134.18

8 0

3 years ago

Alejandra currently has a balance of $2,254 in her checking account. She deposits a $873.84 paycheck, a $25 rebate check, and a

zaharov [31]

Answer:

$3160.84

Step-by-step explanation:

2254 + 873.84 + 25 + 358 = 3510.84

3510.84 - 350 = 3160.84

7 0

3 years ago

System of measure that added prefixes to change the unit’s equivalence??

Stels [109]

Answer:

The metric system is an alternative system of measurement used in most countries, as well as in the United States. The metric system is based on joining one of a series of prefixes, including kilo-, hecto-, deka-, deci-, centi-, and milli-, with a base unit of measurement, such as meter, liter, or gram.

6 0

2 years ago