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2 years ago

Please help me I need it

Mathematics

1 answer:

azamat2 years ago

5 0

Answer: 510 flights

Step-by-step explanation:
85% are expected to arrive on time, so we can convert that to a decimal, which is 0.85. (To convert a percentage to a decimal we can divide by 100.)

After this we take the TOTAL AMOUNT OF FLIGHTS x 0.85
Total Amount = 600

600 x 0.85 = 510.

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The quadratic equation 8x²+12x-14 has two real roots. What is the sum of the squares of these roots?

mars1129 [50]

Answer:

The real roots are

$x=\frac{(-3+\sqrt{37})}{4}$ and $x=\frac{(-3-\sqrt{37})}{4}$

The sum of the squares of these roots is $\frac{-3}{2}$

Step-by-step explanation:

The given quadratic equation is $8x^2+12x-14$ has two real roots.

To find the roots .

$8x^2+12x-14=0$

Dividing the above equation by 2

$\frac{1}{2}(8x^2+12x-14)=\frac{0}{2}$

$4x^2+6x-7=0$

For quadratic equation $ax^2+bx+c=0$ the solution is $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Where a and b are coefficents of $x^2$ and x respectively, c is a constant.

For given quadratic equation

a=4, b=6, c=-7

$x=\frac{-6\pm\sqrt{6^2-4(4)(-7)}}{2(4)}$

$=\frac{-6\pm\sqrt{36+112}}{8}$

$=\frac{-6\pm\sqrt{148}}{8}$

$=\frac{-6\pm\sqrt{37\times 4}}{8}$

$=\frac{-6\pm\sqrt{37}\times\sqrt{4}}{8}$

$=\frac{-6\pm\sqrt{37}\times 2}{8}$

$=2\frac{(-3\pm\sqrt{37})}{8}$

$=\frac{-3\pm\sqrt{37}}{4}$

$x=\frac{(-3\pm\sqrt{37})}{4}$

The real roots are

$x=\frac{(-3+\sqrt{37})}{4}$ and $x=\frac{(-3-\sqrt{37})}{4}$

Now to find the sum of the squares of these roots

$\left[\frac{-3+\sqrt{37}}{4}+\frac{(-3-\sqrt{37})}{4}\right]^2=\frac{-3+\sqrt{37}-3-\sqrt{37}}{4}$

$=\frac{-6}{4}$

$=\frac{-3}{2}$

$\left[\frac{-3+\sqrt{37}}{4}+\frac{(-3-\sqrt{37})}{4}\right]^2=\frac{-3}{2}$

Therefore the sum of the squares of these roots is $\frac{-3}{2}$

3 0

3 years ago

On two examinations, you have grades of 87 and 86. There is an optional final examination, which counts as one grade. You decide

noname [10]

Step-by-step explanation:

We have

87+86+x

T is the total scores

n is number of tests done = 3

T/n is greater than or equal to 90

To get minimum test

T/n = 90

T = 90*n

= 90n

We solve for x

Remember n = 3

90x3 = 270

270 = 87+86+x

270 = 173+x

X = 270-173

X = 97

You didn't add a value in your part b question. I used 80 though.

T/n < 80

T<80n

80x3= 240

T<240

87+86+x<240

X<240-173

X<67

X has to be less than 67 so we conclude that if x <=67 b grade will be lost.

3 0

3 years ago

One of my factors is 9. The sum of my product of my two factors is 13. What inumber am I?

timofeeve [1]

4 x+9=13 X=4 subtract 9 from the 9 and 13 and 13-9 =4 so x=4

5 0

3 years ago

5(x+2)=6x+3x-14 please solve

zavuch27 [327]

Answer:

5(x+2)=6x+3x−14

Step 1: Simplify both sides of the equation.

5(x+2)=6x+3x−14

(5)(x)+(5)(2)=6x+3x+−14(Distribute)

5x+10=6x+3x+−14

5x+10=(6x+3x)+(−14)(Combine Like Terms)

5x+10=9x+−14

5x+10=9x−14

Step 2: Subtract 9x from both sides.

5x+10−9x=9x−14−9x

−4x+10=−14

Step 3: Subtract 10 from both sides.

−4x+10−10=−14−10

−4x=−24

Step 4: Divide both sides by -4.

−4x

−4

−24

−4

x=6

Answer:

x=6

7 0

3 years ago

Help please solve this

NemiM [27]

RU is a diameter, so the two equations make half a circle which is 180 degrees.

24x+5 + 10x+5 = 180

Combine like terms:

34x + 10 = 180

Subtract 10 from both sides:

34x = 170

Divide both sides by 34

X= 5

RS= UV

RS = 10x +5

Replace x with 5

RS = 10(5) + 5 = 55

Answers:

X = 5

RS = 55

4 0

4 years ago

Please help me I need it​

Please help me I need it