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3 years ago

Solve each equation. 8x2 - 24 = 3x2 - 9

Mathematics

2 answers:

blondinia [14]3 years ago

8 0

Answer: The answer is $x=\pm\sqrt{3}.$ .

Step-by-step explanation: The given equation is

$8x^2-24=3x^2-9.$

We are given to solve the above quadratic equation. Since there is no term containing 'x', so we will be using the square root method to solve the equation.

The solution is as follows:

$8x^2-24=3x^2-9\\\\\Rightarrow 8x^2-3x^2=-9+24\\\\\Rightarrow 5x^2=15\\\\\Rightarrow x^2=3\\\\\Rightarrow x=\pm\sqrt{3}.$

Thus, the required solution is $x=\pm\sqrt{3}.$

MariettaO [177]3 years ago

5 0

Ok I'm not sure on how I would do the last bit of the equation but here's what I've got;

Answer 1=                    -8 = -3

Answer2=                    -8 - 3= -11

Not 100% sure on this. so, I'm sorry if its wrong

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Petra started with a number added 3 multiplied the result by 4 subtracted 6 and multiplied that result by 3 her final answer was

dlinn [17]

We don't know the number she started with, so let's call it x.

Petra started with a number added 3: x + 3

multiplied the result by 4: 4(x + 3)

subtracted 6: 4(x + 3) - 6

and multiplied that result by 3: 3[4(x + 3) - 6]

her final answer was 90: 3[4(x + 3) - 6] = 90

Now we solve the equation for x.

3[4(x + 3) - 6] = 90

4(x + 3) - 6 = 30

4(x + 3) = 36

x + 3 = 9

x = 6

The number is 6.

4 0

3 years ago

What regression model best fits the data set?(2,13),(4,8),(5,7.5),(7,9),(8,12)

icang [17]

Answer-

Quadratic Regression model best fits the data set.

Solution-

Taking x as input variable and y as output variable, regression models were obtained by using Excel.

As we can be seen that, the values of y is neither consistently increasing or decreasing ( as 13 > 8 > 7.5 < 9 < 12 ), so exponential growth and exponential decay are of no use (because in exponential function the growth or decay rate is constant).

And also, it can not be linear, as the rate of change of y is not constant.

As we can obtain the correct regression model, by considering Co-efficient of Determination (R²). The value of R² ranges from 0 to 1. The more closer its value to 1, the better the regression model is.

From the attachment, it can be observed that,

$=0.006$

$=R^2_{\text{Exponential}}$

As the value of R² of the Quadratic Regression is more closer to 1, so that should be followed.

7 0

3 years ago

it takes 1/2 of a box of nails to build a bird house if you wanted to build 5 bird houses how many boxes would you need

dedylja [7]

Answer:

You would need 2.5

Step-by-step explanation:

You can use a porportion to solve.

$\frac{.5}{1} = \frac{x}{5}$ (cross multiply and solve)

7 0

3 years ago

Part A- Create a fourth degree polynomial in standard form. How do you know it is in standard form?

Alexeev081 [22]

Answer:

(a) $2x^4-9x^3+x^2+x-5$

Step-by-step explanation:

(a)The degree of a polynomial is the highest power of the unknown variable in the polynomial.

A polynomial is said to be in standard form when it is arranged in descending order/powers of x.

An example of a fourth degree polynomial is: $2x^4-9x^3+x^2+x-5$

We know the polynomial above is in standard form because it is arranged in such a way that the powers of x keeps decreasing.

(b)Polynomials are closed with respect to addition and subtraction. This is as a result of the fact that the powers do not change. Only the coefficients

change. This is illustrated by the two examples below:

$(2x^5-3x^2+x)+(3x^5-5x^2)\\=2x^5-3x^2+x+3x^5-5x^2\\=5x^5-8x^2+x\\$Similarly\\(2x^5-3x^2+x)-(3x^5-5x^2)\\=2x^5-3x^2+x-3x^5+5x^2\\=-x^5+2x^2+x$

The degrees do not change in the above operations. Only the number beside each variable changes. Therefore, the addition and subtraction of polynomials is closed.

7 0

2 years ago

My soccer team has 16 players. I have to choose a starting lineup of a goalie and 10 regular players (the regular players are in

ASHA 777 [7]

Answer:

3003

Step-by-step explanation:

We want to find out how many ways we can choose 10 players among 15 players (since the goalie is not interchangeable)

The number of different lineups you can have can be found by using combination:

$^{15}C_{10} = \frac{15!}{(15 - 10)! 10!}\\ \\= \frac{15!}{5! * 10!} \\\\= 3003$

There are 3003 different lineups that can be chosen.

6 0

3 years ago