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oksano4ka [1.4K]
2 years ago
13

Find (x + 4)(x2 + x - 2). Write your answer in standard form. Answer please

Mathematics
1 answer:
ahrayia [7]2 years ago
3 0

Answer:

X^3 + 5x^2 + 2x - 8

Step-by-step explanation:

You might be interested in
The sides of a right triangle have a relationship as depicted below, where x is the length of the longer leg in inches.
Ratling [72]
The equation to represent the area of the triangle would be:
y = 1/2(x²) - (7/2)x

The equation to represent the perimeter of the triangle would be:
y = 3x - 6

The solutions to the system would be (12, 30) or (1, -3).  The only viable solution is (12, 30).

Explanation
The area of a triangle is found using the formula
A = 1/2bh

For our triangle, b = x and h = x-7, so we have:
A = 1/2(x)(x-7)
A = 1/2(x²-7x)
A = 1/2(x²) - (7/2)x

We will replace A with y, so we have:
y = 1/2(x²) - (7/2)x

The perimeter of a triangle is found by adding together all sides, so we have:
P = (x-7) + x + (x+1)

Combining like terms we get:
P = 3x - 6

We will replace P with y, so we have:
y = 3x - 6

Since both equations have y isolated on one side, it will be easy to use substitution to solve the system:

3x - 6 = 1/2(x²) - (7/2)x

It's easier to work with whole numbers, so we will multiply everything by 2:
6x - 12 = x² - 7x

We want all of the variables on one side, so we will subtract 6x:
6x - 12 - 6x = x² - 7x - 6x
-12 = x² - 13x

When solving quadratics, we want the equation equal to 0, so we will add 12:
-12+12 = x² - 13x + 12
0 = x² - 13x + 12

This is easy to factor, as there are factors of 12 that sum to -13; -12(-1) = 12 and -12+-1 = -13:
0 = (x-12)(x-1)

Using the zero product property, we know that either x-12=0 or x-1=0; therefore x=12 or x=1.

Putting these back into our equation for perimeter (the simplest one) we have:
y = 3(12)-6 = 36-6 = 30; (12, 30);
y = 3(1) - 6 = 3 - 6 = -3; (1, -3)

We cannot have a negative perimeter, so the only viable solution is (12, 30).
8 0
2 years ago
If x = 10, what is the first step you would do to answer 3x 2
Vinvika [58]

Answer:

300

Step-by-step explanation:

X^2=10×10=100

3×100=300

3 0
3 years ago
15 and 16 please help
Ymorist [56]
15.
if he ordered  the same amount each month (x) and it is a whole number,
then
12*x=6150, and 
x =6150/12 should be a whole number
x=512.5
so 512.5 is not a whole number and the produce company does not agree

16.
16410/138≈118.91
because it not a whole number, she sells pieces for different prices
6 0
3 years ago
No links plz! Will mark brainliest if correct!
ehidna [41]

Answer:

(m-4) / (5m)

Step-by-step explanation:

((m²-16) / (5m)) / (m+4) =

(m²-16) / (5m(m+4)) =

m²-16 / (5m²+20m) =

(m-4) / (5m)

7 0
2 years ago
We take a milk carton from the refrigerator and put it on the table at room temperature. We assume that the temperature of the c
Kisachek [45]
We can solve this problem using separation of variables.

Then apply the initial conditions

EXPLANATION

We were given the first order differential equation

\frac{dT}{dt}=k(T-a)

We now separate the time and the temperature variables as follows,

\frac{dT}{T-a}=kdt

Integrating both sides of the differential equation, we obtain;

ln(T-a)=kt +c

This natural logarithmic equation can be rewritten as;

T-a=e^{kt +c}

Applying the laws of exponents, we obtain,

T-a=e^{kt}\times e^{c}

T-a=e^{c}e^{kt}

We were given the initial conditions,

T(0)=4

Let us apply this condition to obtain;

4-20=e^{c}e^{k(0)}

-16=e^{c}

Now our equation, becomes

T-a=-16e^{kt}

or

T=a-16e^{kt}

When we substitute a=20,
we obtain,

T=20-16e^{kt}

b) We were also given that,

T(5)=8

Let us apply this condition again to find k.

8=20-16e^{5k}

This implied

-12=-16e^{5k}

\frac{-12}{-16}=e^{5k}

\frac{3}{4}=e^{5k}

We take logarithm to base e of both sides,

ln(\frac{3}{4})=5k

This implies that,

\frac{ln(\frac{3}{4})}{5}=k


k=-0.2877

After 15 minutes, the temperature will be,


T=20-16e^{-0.2877\times 15}

T=20-0.21376


T=19.786

After 15 minutes, the temperature is approximately 20°C


6 0
3 years ago
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