MATHEMATICS HIGH SCHOOL

4k^2(-3k^2 - 4k + 5) A. -12k^4 - 16k^3 + 20k^2
B. 12k^4 - 16k^3 + 9k^2
C. -12k^3 + 20k
D. k^4 + 9k^2

Answers

Answer 1
Answer: Hello,

Answer A for 4k²*5=20k²
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How do I solve a quadratic equation like this: x squared minus 9x = -14?

Answers

x^2-9x=-14\n\nx^2-9x+14=0\n--------------------\n-9=-7+(-2)\n14=-7\cdot(-2)\n--------------------\n\nx^2-9x+14=(x-7)(x-2)\n\n(x-7)(x-2)=0\iff x-7=0\ or\ x-2=0\n\nx=7\ or\ x=2



x^2-9x+14=0\n\na=1;\ b=-9;\ c=14\n\n\Delta=b^2-4ac\n\n\Delta=(-9)^2-4\cdot1\cdot14=81-56=25\n\nx_1=(-b-\sqrt\Delta)/(2a)\to x_1=(9-√(25))/(2\cdot1)=(9-5)/(2)=(4)/(2)=2\n\nx_2=(-b+\sqrt\Delta)/(2a)\to x_2=(9+√(25))/(2\cdot1)=(9+5)/(2)=(14)/(2)=7
Bring everything over to one side.
    x² -9x=-14
x²-9x+14=0
Now it is an easy trinomial so you need to find two numbers that add up to -9 and multiply to equal 14. The two numbers are -7 and -2. 
 x²-9x+14=0
 (x-7)(x-2)=0
            x= 7 and 2

If a man take one and a half mins to paint a door how much doors can he paint in seven half hour

Answers

Answer:

300 doors.

Step-by-step explanation:

1.5 minutes for 1 door.

7.5 hours for 300 doors.

7.5 hours = 450 minutes.

(450)/(1.5)=300

The length of a rectangle is 5 5 centimeters less than six times six times its width. Its area is 14 14 square centimeters. Find the dimensions of the rectangle.

Answers

Answer:

Dimensions of rectangle are length = 7 cm and width = 2 cm

Step-by-step explanation:

Let l = length and w = width of the rectangle.

Given that, length is 5 cm less than 6 times width. Rewriting it in equation form,

L =  6 w - 5  cm

Also given that area of rectangle is 14 cm²

Now using formula for area of rectangle,

Area of rectangle = length × width

Area of rectangle = l × w

Substituting the values,

14 = (6 w - 5) × w

Simplifying by using distributive rule,

14 = 6 w² - 5 w

To find the value of b, use the quadratic formula. So rewriting the equation in quadratic form ax²+bx+c=0

Subtracting 14 on both sides,

0 = 6 w² - 5 w - 14

Rewriting,

6 w² - 5 w - 14  = 0

Now applying quadratic formula,

x=(-b\pm √(b^2-4ac))/(2a)

Rewriting the formula in terms of w,

w=(-b\pm √(b^2-4ac))/(2a)

From the 6 w² - 5 w - 14  = 0, value of a = 6 , b = - 5 and c = - 14.

Substituting the values,

w=(-\left(-5\right)\pm √(\left(-5\right)^2-4\cdot \:6\left(-14\right)))/(2\cdot \:6)

Simplifying,

w=(-\left(-5\right)\pm √(25+336))/(12)

w=(-\left(-5\right)\pm √(361))/(12)

Since √361 = 19,

w=(-\left(-5\right)\pm 19)/(12)

There will be two values of w,

w=(-\left(-5\right)+19)/(12) and w=(-\left(-5\right)-19)/(12)

Simplifying,

w=(5+19)/(12) and w=(5-19)/(12)

w=(24)/(12) and w=(-14)/(12)

Reducing the fraction in lowest form, divide first expression by 12 and second expression by 2.

w=2 and w=(-7)/(6)

Since the length of width cannot be negative, so value of w = 2 cm

To find the value of length, Use equation L =  6 w - 5  cm

L =  6 (2) - 5  cm

L =  12 - 5  cm

L =  7  cm

Therefore l = 7 cm and w = 2 cm are the dimensions of the rectangle.

An electrician has a spool of wire that is 200 m long. she needs four pieces of wire measuring 42.3 m, 37.8 m, 55.6 m, and 35.7 m. about how much wire will be left on the spool after she finishes her job? give your answer with the appropriate precision.

Answers

She needs exactly 42.3m + 37.8m + 55.6m + 35.7m = 171.4m for accomplishing her job, so there will be 28.6 m  (200m-171.4m)  of wire after she finished her work.

Please help me w/ this geometry question.

image attached.

Answers


The \: answer \: is \: 46 °

Follow the steps in purple to evaluate:4
+
9
To add or subtract fractions, their denominators
must be the same. We can get a common
denominator by multiplying the second fraction
by 3/3.
6
-
(-}).
What number belongs in the green box?
Enter

Answers

I think it is 3 but I’m not 100%
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