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3 years ago

Match these items. need help asap!!!

Mathematics

1 answer:

Black_prince [1.1K]3 years ago

3 0

Answer:

1.energy

2.lightning

3.matter

4.fuel

5.solar energy

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Among all pairs of numbers (x,y) such that 3x+y=15, find the pair for which the sum of squares, x^2+y^2, is minimum. Write your

Dvinal [7]

Answer:

Minimum value occurs at (x, y) = (-5,0)

Step-by-step explanation:

Given: 3x + y =15

Rewriting this equation to Slope - Intercept form, we get:

y = -3x + 15

Squaring both sides,

$y^2 = (-3x + 15)^2$

$\implies y^2 = 9x^2 - 90x + 225$

Substituting in $x^2 + y^2,$ we get:

$x^2 + 9x^2 - 90x + 225$

= $10x^2 - 90x + 225$

Comparing this equation with $ax^2 + bx + c$ we get $a =10$ and $b = - 90$ .

The minimum value occurs at the axis of symmetry given by $x = \frac{-b}{2a}$ .

Therefore, x = - $\frac{-90}{2.10}$

$\implies x = 5$

If x = 5, y = -3(5) + 15 = 0

Thus, the point becomes (5,0) where it is minimum.

5 0

4 years ago

What number between 121 and 149 is exactly divisible by both 3 and 5

Komok [63]

Answer:

135

Step-by-step explanation:

135 by 3 is 45

by 5 is 27

3 0

3 years ago

Read 2 more answers

Find the missing sides.

love history [14]

Answer:

Part 3)

$x=6\ units$

$y=3\ units$

Part 4) $x=18\sqrt{2}\ units$

Step-by-step explanation:

Part 3)

Find the value of x

In the right triangle of the figure we know that

The cosine of angle of 30 degrees is equal to the adjacent side to angle of 30 degrees divide by the hypotenuse

$cos(30\°)=\frac{3\sqrt{3}}{x}$

and remember that

$cos(30\°)=\frac{\sqrt{3}}{2}$

substitute

$\frac{\sqrt{3}}{2}=\frac{3\sqrt{3}}{x}$

Simplify

$x=(2*3)=6\ units$

Find the value of y

In the right triangle of the figure we know that

The sine of angle of 30 degrees is equal to the opposite side to angle of 30 degrees divide by the hypotenuse

$sin(30\°)=\frac{y}{x}$

and remember that

$sin(30\°)=\frac{1}{2}$

substitute

$\frac{1}{2}=\frac{y}{6}$

$y=6/2=3\ units$

Part 4) Find the value of x

Applying the Pythagoras Theorem

$x^{2} =18^{2} +18^{2} \\ \\x^{2} = 324+324\\ \\x^{2}=648\\ \\x=\sqrt{648}\ units$

Simplify

$x=18\sqrt{2}\ units$

6 0

3 years ago

Find the value of x so that f(x) = 13 when f(x) = 3x + 4

maksim [4K]

Answer:

Step-by-step explanation:

13=3x+4

subtract 4 from both sides

9=3x

divide by 3

x=3

5 0

3 years ago

in a box there are 6 red, 8 green, and 10 white balls. if three balls are selected simultaneously and at random and the color is

katovenus [111]

Make them into fractions. Red=6/24 Green:8/24 White:10/24. Why is it 24 is a denominator? Because 10+8+6=24. About how many times does 3 go into 8? 2 times. Which means the Probability of green is: 2/24

3 0

4 years ago