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lozanna [386]
3 years ago
13

The GCD of two numbers is 29 and their LCM is 348 One of the numbers is 87. Find the other number.

Mathematics
1 answer:
Oksanka [162]3 years ago
8 0

hi tfycuch ych y hcy g gh n j j j j jvi hcnch h n j h jcj

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Write an equation of a parabola that passes through (3,-30) and has x-intercepts of -2 and 18. Then find the average rate of cha
Nookie1986 [14]

Answer:

The equation of the parabola is y = \frac{2}{5}\cdot x^{2}-\frac{32}{5}\cdot x -\frac{72}{5}.  The average rate of change of the parabola is -4.

Step-by-step explanation:

We must remember that a parabola is represented by a quadratic function, which can be formed by knowing three different points. A quadratic function is standard form is represented by:

y = a\cdot x^{2}+b\cdot x + c

Where:

x - Independent variable, dimensionless.

y - Dependent variable, dimensionless.

a, b, c - Coefficients, dimensionless.

If we know that (3, -30), (-2, 0) and (18, 0) are part of the parabola, the following linear system of equations is formed:

9\cdot a +3\cdot b + c = -30

4\cdot a -2\cdot b +c = 0

324\cdot a +18\cdot b + c = 0

This system can be solved both by algebraic means (substitution, elimination, equalization, determinant) and by numerical methods. The solution of the linear system is:

a = \frac{2}{5}, b = -\frac{32}{5}, c = -\frac{72}{5}.

The equation of the parabola is y = \frac{2}{5}\cdot x^{2}-\frac{32}{5}\cdot x -\frac{72}{5}.

Now, we calculate the average rate of change (r), dimensionless, between x = -2 and x = 8 by using the formula of secant line slope:

r = \frac{y(8)-y(-2)}{8-(-2)}

r = \frac{y(8)-y(-2)}{10}

x = -2

y = \frac{2}{5}\cdot (-2)^{2}-\frac{32}{5}\cdot (-2)-\frac{72}{5}

y(-2) = 0

x = 8

y = \frac{2}{5}\cdot (8)^{2}-\frac{32}{5}\cdot (8)-\frac{72}{5}

y(8) = -40

r = \frac{-40-0}{10}

r = -4

The average rate of change of the parabola is -4.

3 0
3 years ago
What is the measure of X? <br> angles are not necessarily drawn to scale
Schach [20]

Answer:

xº=71º

Step-by-step explanation:

Take the triangle BDH

Once the sum of interior angles of a triangle is 180º:

40º+31º+yº=180º

71º+yº=180º

yº=109º

Once yº and xº are supplementary angles (add up to 180º):

yº+xº=180º

109º+xº=180º

xº=71º

5 0
3 years ago
if you have driving 120 miles per hour how much more miles per hour do you need to drive to get to 208
Verizon [17]

Answer:

I think it would be 88

Step-by-step explanation:

208-120=88

hope this helps! :)

6 0
2 years ago
Need help with the last three asap
Sunny_sXe [5.5K]
13) Angle 1= 54 Angle 2=36
14) Angle 1=122 Angle 2=58
15) Angle 1=51 Angle 2=39
Attached is the work
Hope this helps!

7 0
3 years ago
WikiTongues has
konstantin123 [22]

Hey there! I'm happy to help!

We see that 500 languages is a certain percent of the 7,111 total languages. When working with percent equations, the word "is" means "equals", and "of" usually means "multiplied by" This means that 500 is equal to a certain percent multiplied by 7,111. We can use p to represent this certain percent and create an equation below.

500=7,111p

Let's flip the equation around so the p is on the left side. Variables are usually supposed to be on the left.

7,111p=500

We divide both sides by 7,111.

p=0.0703

As a percent, this is about 7.03%. Therefore, about 7.03% of the total languages spoken globally are represented on WikiTongues.

I hope that this helps! Have a wonderful day! :D

3 0
3 years ago
Read 2 more answers
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