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2 years ago

Functions assignment Y= 2/3x+20 When x=21 what is the function and solution

Mathematics

1 answer:

Nonamiya [84]2 years ago

3 0

Answer:

y = 2/3 (21) + 20 (plug it in and multiply)

y = 14 +20 (add)

y = 34

(21,34)

Step-by-step explanation:

i hope this helps :)

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At the grocery store, Luis brought 10 bananas and 4 apple. What are three different ways to write the 4 ratio of apples to banan

Reil [10]

10/4, 4:10 and, 10 to 4.
If that helps make sure to 5 star and brainliest! <3

-Procklownyt

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2 years ago

Your sock drawer has 3 pairs of black socks, 4 pairs of brown socks, 1 pair of yellow socks and 5 pairs of blue socks. you reach

erik [133]

All socks together: 13
Black socks: 3

Probability to pick out black socks: 3/13

After one pick out (You picked out a pair of black socks):

Probability to pick out black socks: 2/12

Multiply them:

2/12 * 3/13 = 1/26 ≈ 0,038

8 0

2 years ago

Triangle ABC is shown below.

Andrew [12]

Answer:

C.) 14

Step-by-step explanation:

Look at the triangle: angles b and c have the same arch, so they are congruent.

In a triangle, if two angles are congruent, then the triangle is isosceles, having two equal sides.

The sides opposite the congruent angles are congruent:

∠B → opposite side → AC

∠C → opposite side → AB

The sides AB and AC are equal. Make an equation:

$AB=AC\\\\2x=3x-7$

Simplify the equation, solving for x. Add 7 to both sides:

$2x+7=3x-7+7\\\\2x+7=3x$

Subtract 2x from both sides:

$2x-2x+7=3x-2x\\\\7=x$

The value of x is 7. Insert the value of x into the given length of AC:

$AC=3(7)-7$

Simplify multiplication:

$AC=21-7$

Subtract:

$AC=14$

Therefore, the length of the line segment AC is 14.

:Done

8 0

2 years ago

What is the answer?<br><br> Y=x-6 and y=2x

Rashid [163]

$\begin{cases}y=x-6\\y=2x\end{cases}\implies~x-6=2x\implies~x=-6$

which means

$y=x-6=y=-6-6=-12$

4 0

2 years ago

Read 2 more answers

A box with a hinged lid is to be made out of a rectangular piece of cardboard that measures 3 centimeters by 5 centimeters. Six

kherson [118]

Answer:

x = 0.53 cm

Maximum volume = 1.75 cm³

Step-by-step explanation:

Refer to the attached diagram:

The volume of the box is given by

$V = Length \times Width \times Height \\\\$

Let x denote the length of the sides of the square as shown in the diagram.

The width of the shaded region is given by

$Width = 3 - 2x \\\\$

The length of the shaded region is given by

$Length = \frac{1}{2} (5 - 3x) \\\\$

So, the volume of the box becomes,

$V = \frac{1}{2} (5 - 3x) \times (3 - 2x) \times x \\\\V = \frac{1}{2} (5 - 3x) \times (3x - 2x^2) \\\\V = \frac{1}{2} (15x -10x^2 -9 x^2 + 6 x^3) \\\\V = \frac{1}{2} (6x^3 -19x^2 + 15x) \\\\$

In order to maximize the volume enclosed by the box, take the derivative of volume and set it to zero.

$\frac{dV}{dx} = 0 \\\\\frac{dV}{dx} = \frac{d}{dx} ( \frac{1}{2} (6x^3 -19x^2 + 15x)) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\0 = \frac{1}{2} (18x^2 -38x + 15) \\\\18x^2 -38x + 15 = 0 \\\\$

We are left with a quadratic equation.

We may solve the quadratic equation using quadratic formula.

The quadratic formula is given by

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Where

$a = 18 \\\\b = -38 \\\\c = 15 \\\\$

$x=\frac{-(-38)\pm\sqrt{(-38)^2-4(18)(15)}}{2(18)} \\\\x=\frac{38\pm\sqrt{(1444- 1080}}{36} \\\\x=\frac{38\pm\sqrt{(364}}{36} \\\\x=\frac{38\pm 19.078}{36} \\\\x=\frac{38 + 19.078}{36} \: or \: x=\frac{38 - 19.078}{36}\\\\x= 1.59 \: or \: x = 0.53 \\\\$

Volume of the box at x= 1.59:

$V = \frac{1}{2} (5 – 3(1.59)) \times (3 - 2(1.59)) \times (1.59) \\\\V = -0.03 \: cm^3 \\\\$

Volume of the box at x= 0.53:

$V = \frac{1}{2} (5 – 3(0.53)) \times (3 - 2(0.53)) \times (0.53) \\\\V = 1.75 \: cm^3$

The volume of the box is maximized when x = 0.53 cm

Therefore,

x = 0.53 cm

Maximum volume = 1.75 cm³

7 0

2 years ago