MATHEMATICS HIGH SCHOOL

Evaluate the limit, if it exists. Show work.
lim→5 2−3−10 / 2−10

Answers

Answer 1
Answer:

Answer:

Convert the mixed numbers to improper fractions, then find the LCD and combine.

Exact Form: 13/3

Decimal Form:  4.3

Mixed Number Form:4  1/3

Step-by-step explanation:

Hope this helps ;)

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A balloon lifts off the ground and reaches a height of 200m. The total mass of the balloon is 1000 kg. What is the GPE of the balloon?

Answers

Answer:

1,960,000Joules

Step-by-step explanation:

Gravitational Potential Energy is expressed as;

GPE = mgh

m is the mass

g is the acceleration due to gravity

h is the height

Given

m = 1000kg

h = 200m

g = 9.8m/s

Substitute;

GPE  = 1000 * 9.8 * 200

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GPE = 1,960,000Joules

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What are the solutions of this quadratic equation? x^2+13=8x+37

Answers

The solutions of the quadratic equation x² + 13 = 8x + 37 are x = 4 + 2√10 and x = 4 - 2√10.

What is a quadratic equation?

The quadratic equation is defined as a function containing the highest power of a variable is two.

The given equation as:

x² - 8x + 13 = 37

Subtracting 37 from both sides, we get:

x² - 8x - 24 = 0

Now, we have the equation in standard form, so we can use the quadratic formula to find the solutions:

x = (-b ± √(b² - 4ac)) / 2a

Here, a = 1, b = -8, and c = -24.

Substitute these values into the quadratic formula, and we get:

x = (-(-8) ± √((-8)² - 4(1)(-24))) / 2(1)

x = (8 ± √(64 + 96)) / 2

x = (8 ± √160) / 2

x = (8 ± 4√10) / 2

Simplifying, we get:

x = 4 ± 2√10

Therefore, the solutions of the quadratic equation x² + 13 = 8x + 37 are x = 4 + 2√10 and x = 4 - 2√10.

Learn more about quadratic function here:

brainly.com/question/14083225

#SPJ3

Answer:

              x\in\left\{4-2√(10)\ ,\ \,4+2√(10)\,\right\}

Step-by-step explanation:

x^2+13=8x+37\n\nx^2-8x-24=0\n\na=1\,,\ \ b=-8\,,\ \ c=-24\n\nx_1=(-(-8)-√((-8)^2-4\cdot1\cdot(-24)))/(2\cdot1)=\frac{8-√(64+96)}2=\frac{8-√(160)}2 =\n\n=\frac{8-4√(10)}2=\frac{2(4-2√(10))}2=4-2√(10) \n\nx_2=(-(-8)-√((-8)^2-4\cdot1\cdot(-24)))/(2\cdot1)=\frac{8+4√(10)}2=4+2√(10)

True or False it's possible to build a triangle with side lengths of 5,5, and 10.

Answers

It's not possible, because the sum of the lenghts of every two sides of a triangle has to be greater than the length of the third one. It this case that condition isn't met: 5+5\not>10

The answer to this question is False

Find the perimeter of an isosceles trianglewhose base is  40  cm and whose base angle is  70".

Answers

cos70^o=(20)/(x)\n\ncos70^o\approx0.342\n\n(20)/(x)=0.342\n\n0.342x=20\ \ \ \ /:0.342\n\nx\approx58.5\ (cm)\n\nPerimeter:40cm+2\cdot58.5cm=157cm
cos70^0= (20)/(x)\n\nx= (20)/(cos70^0) \n\nthe\ perimeter\ is:\n\n P=2x+40=(40)/(cos70^0)+40 \ \ \ and\ \ \ cos70^0\approx0.3420\n\nP\approx(40)/(0.342)+40\approx156.96\ [cm]

What is the measure of side RS ​

Answers

Answer:

57

Step-by-step explanation:

5y - 33 = 57.

Add 33.

5y = 90

Divide by five.

y = 18

5(18) - 33 = 57

If 120% is 360,what is 100%

Answers

Answer:

300

Step-by-step explanation:

We know

120% = 360

100% = ?

We cross multiply by 100 and divide by 120.

(360 x 100) ÷ 120 = 300

So, the answer is 300
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