Please help will mark brainliest

Topic: The Quadratic Formula

Finger [1]

Answer:

Step-by-step explanation:

The quadratic formula for a equation of form

ax²+bx + c = 0 is

$x= \frac{-b +- \sqrt{b^2-4ac} }{2a}$

For the first equation,

x²+3x-4=0,

we can match that up with the form

ax²+bx + c = 0

to get that

ax² = x²

divide both sides by x²

a=1

3x = bx

divide both sides by x

3 = b

-4 = c

. We can match this up because no constant multiplied by x could equal x² and no constant multiplied by another constant could equal x, so corresponding terms must match up.

Plugging our values into the equation, we get

$x= \frac{-3 +- \sqrt{3^2-4(1)(-4)} }{2(1)} \\= \frac{-3+-\sqrt{25} }{2} \\ = \frac{-3+-5}{2} \\= -8/2 or 2/2\\= -4 or 1$

as our possible solutions

Plugging our values back into the equation, x²+3x-4=0, we see that both f(-4) and f(1) are equal to 0. Therefore, this has 2 real solutions.

Next, we have

x²+3x+4=0

Matching coefficients up, we can see that a = 1, b=3, and c=4. The quadratic equation is thus

$x= \frac{-3 +- \sqrt{3^2-4(1)(4)} }{2(1)}\\= \frac{-3 +- \sqrt{9-16} }{2}\\= \frac{-3 +- \sqrt{-7} }{2}\\$

Because √-7 is not a real number, this has no real solutions. However,

(-3 + √-7)/2 and (-3 - √-7)/2 are both possible complex solutions, so this has two complex solutions

Finally, for

4x² + 1= 4x,

we can start by subtracting 4x from both sides to maintain the desired form, resulting in

4x²-4x+1=0

Then, a=4, b=-4, and c=1, making our equation

$x=\frac{-(-4) +- \sqrt{(-4)^2-4(4)(1)} }{2(4)} \\= \frac{4+-\sqrt{16-16} }{8} \\= \frac{4+-0}{8} \\= 1/2$

Plugging 1/2 into 4x²+1=4x, this works as the only solution. This equation has one real solution

7 0

2 years ago

If there are 300 fish in a pond and 6 of them get eaten how many is left

sweet-ann [11.9K]

Answer:

294

Step-by-step explanation:

8 0

2 years ago

HELP Sam measures the height of 7 different scoops of ice cream. The mean of the heights was 3.8 cm. Which of the following best

OLga [1]

Sam measures the height of 7 different scoops of ice cream. The mean height was 3.8 cm. If all the scoops are evenly distributed, they would all be 3.8 cm tall.

<h3>How to find the mean value of a data set?</h3>

The mean value of the data set is the ratio of the sum of the data set's values to the number of values it has.

If the data set consists of values

x_1, x_2, ..., x_n

, then we get the mean value as:

$\overline{x} = \dfrac{x_1 + x_2 + \cdots + x_n}{n}$

Sam measures the height of 7 different scoops of ice cream. The mean height was 3.8 cm.

$\overline{x} = \dfrac{x_1 + x_2 + \cdots + x_n}{n}$

mean= $\dfrac{(a+b+c+d+e+f+g)}{7}$

Therefore, If all the scoops are evenly distributed, they would all be 3.8 cm tall.

Learn more about mean;

brainly.com/question/23008823

#SPJ2

8 0

2 years ago

Read 2 more answers

The area of a square can be found using the equation A= s^2, where A is he area and s is the measure of one side of the square.

Kamila [148]

side length of the square can be written simply : $\sqrt{99}$

5 0

3 years ago

Don't know how to solve this please help. Show work, thank you

anyanavicka [17]

Hello!

We know that the sum of the three angles of a triangle is equal to 180 degrees. This can be represented using the following formula:

A1 + A2 + A3 = 180

With this knowledge, we can successfully find the missing measurements.

We’ll begin with the large right triangle. Because it is a right triangle, we know that one of its angles is equal to 90 degrees. We are also given that its second angle has a measure of 65 degrees. Insert this information into the formula above and combine like terms:

(90) + (65) + A3 = 180
155 + A3 = 180

Now subtract 155 from both sides of the equation:

A3 = 25

We have now proven that the third angle has a measure of 25 degrees. Looking at the provided image, you’ll notice that this 25 degree angle is adjacent to the 80 degree angle. We can add these neighboring angles to find one of the missing angles of the medium triangle:

25 + 80 = 105

We have now proven that this larger angle has a measure of 105 degrees. Looking again at the provided image, you’ll notice that this triangle also contains a 50 degree angle. Using the “three-angles” formula, we can find the remaining angle of the medium triangle. Insert any known values and combine like terms:

(105) + (50) + A3 = 180
155 + A3 = 180

Now subtract 155 from both sides of the equation:

A3 = 25

We have now proven the third angle of the medium triangle to have a measure of 25 degrees. Consequently, we now have now proven two of the three angles of the smallest triangle. Again using the “three-angles” formula, we can find the measure of the missing angle (x). Insert any known values (using the variable “x” to represent the missing angle) and combine like terms:

(25) + (25) + (x) = 180
50 + x = 180

Now subtract 50 from both sides:

x = 130

we have now proven that the missing angle (x) has a measure of 130 degrees.

I hope this helps!
second angle which has a value of 65 degrees.

3 0

2 years ago