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3 years ago

Complete the square for 5x^2+10x-16. first one to answer gets brainiest

Mathematics

1 answer:

ella [17]3 years ago

5 0

Answer: x= -1 + √(21/5)

Step-by-step explanation:

The given equation can be written as 5x^2+10x-16=0

keep the x terms on one side and constant on another side

5x^2+ 10x = 16.

Now, to make a complete square like (x+a)^2 = x^2+2xa+a^2.

Divide the given equation by 5 on both sides,

The equation now becomes x^2+2x = 16/5.

The middle term is 2xa=2x

By solving for term "a" in above equation, a= 1

The entire equation of complete square should be x^2+2x+1, which is equal to (x+1)^2

Here, in the equation given in question, +1 is missing to make a complete square.

In order to add 1 we have to simultaneously minus 1 to keep the values in the equation unchanged.

Thus, x^2+2x+1-1 =16/5.

Again moving the constant -1 to other side, we have

x^2+2x+1 =16/5+1

After simplification,

(x+1)^2= 21/5

Taking square root on both sides,

(x+1)= + √(21/5)

The answer is x= -1 + √(21/5)

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Plz help me .....simplify the ratio of 0,0064kg to 32 grams

Degger [83]

9514 1404 393

Answer:

1/5

Step-by-step explanation:

1 kg = 1000 g so your ratio is ...

$\dfrac{0.0064\text{ kg}}{32\text{ g}}=\dfrac{0.0064\cdot1000\text{ g}}{32\text{ g}}=\dfrac{6.4}{32}=\boxed{\dfrac{1}{5}}$

4 0

3 years ago

Find the solution to the system of linear equations y = 5x + 4 and y = −3x + 12 using the intersection method. Check your answer

Umnica [9.8K]

Answer:

The solution to the system of linear equations is (1,9).

Step-by-step explanation:

The given system of linear equations

$y=5x+4$ ... (1)

$y=-3x+12$ .... (2)

Subtract equation (2) from equation (1) to eliminate y.

$y-y=(5x+4)-(-3x+12)$

$0=5x+4+3x-12$

On combining like terms, we get

$0=(5x+3x)+(4-12)$

$0=8x-8$

Add 8 on both sides.

$0+8=8x-8+8$

$8=8x$

Divide both sides by 8.

$1=x$

The value of x is 1.

Substitute x=1 in equation (1).

$y=5(1)+4$

$y=5+4$

$y=9$

The value of y is 9.

Therefore the solution to the system of linear equations is (1,9).

4 0

3 years ago

Gina saw twice as many tigers as lions at the zoo. The number of bears she saw was 7 less than the number of tigers. She saw fiv

Fynjy0 [20]

Gina saw 25 monkeys
25 ÷ 5 = 5
5 + 7 = 12
12 + 6 = 18
25 + 5 +12 + 6 = 48 animals
gina saw 48 animals at the zoo

8 0

3 years ago

Circles C, B, and P overlap. Circle C contains 9, circle B contains 11, and circle P contains 7. The overlap of circles C and P

Tpy6a [65]

9514 1404 393

Answer:

63 in the class
(C+B)P' = 25
(C+B+P)' = 18

Step-by-step explanation:

The number of students in the class is the total of all numbers on the diagram:

9 +5 +11 +6 +3 +4 +7 +18 = 63 . . . students in the 2015 senior class

Students taking Chem or Biology, but not Physics are those in the colored area, excluding those in the green:

9 +5 +11 = 25 science students not taking Physics

Students not taking science are those outside the colored areas:

18 students are not taking science

6 0

3 years ago

Read 2 more answers

Micheal recorded the number of points his team scored for the first seven basketball games, 64,58,60,52,56,62,54 Which box plot

Ivenika [448]

Answer:

The correct box plot is B (Bottom left)

Step-by-step explanation:

I have attached the appropriate picture containing the box plots to this answer. In order to choose the most appropriate box plot, we have to find the median of the distribution and locate the box plot showing the correct median. This is done as follows:

To find the median, we will first arrange the distribution in ascending (or descending) order

Median = 52, 54, 56, 58, 60, 62, 64

Next, we will group the data into two halves, and choose the middle term, which is 58. this becomes the median.

From the diagram, box plots, A, B and C have their median as 58, in order to determine the correct plot, we will find the medians to the lower and upper halves of the distribution. This is done as follows:

Lower half: 52, 54, 56, 58

Median of lower half = (54 + 56) ÷ 2 = 55

upper half = 58, 60, 62, 64

Median of upper half = (60 + 62) ÷ 2 = 61

From the picture the plot with these three medians from lower half to upper half (55, 58, 61) is plot B (bottom left)

Note the medians are the lines that form the boundaries and at the middle of the box.

6 0

4 years ago